Are Terrans objectively better than Protoss at Aggression/Harass?

First, I'd like to say that racial abilities aside, it's doubtful any of us are using any race's harassment abilities to their max. Thus, the answer is just to harass more, not to switch races. However, if you want an attempt at point-by-point comparison:

Cliff harass

Terran wins early, loses late-game. - Terran reapers are the fastest tier-1 unit (before speedling/charge upgrades). - Protoss blink stalkers with an observer allows much larger cliff harassment late-game.

Drop harass

Terran wins early, debatable late game. - Terran medivacs have speed boost, and heal units, which is great for small engagements. Larger engagements require making many medivacs...but that indeed does happen anyway. Late-game, marines' extremely high dps/cost allows them to keep up as much small-group pressure as you can control. - Protoss can do massive warp-ins late game. High-touch drop harass is more effective with regenerating shields and high-hp units like collosi or immortals...but in reality, warp prisms are often used for a round of throwaway zealots or a few dark templars.

Air harass

I would give this one to Protoss now. In WoL, banshee would just win this category. The oracle has massive dps though, and kills workers even faster than the banshee, with caveats that it has less hp and requires having mana to do its damage. The oracle sucks in combat more than the banshee (lower hp, bonus damage only against one type of unit), but for harassment purposes you're likely killing small units like workers or a few stray light units.

Cloak harassment

Terran wins at first with widow mines and banshees - factory and starport are on your tech pathway anyway. Late game, stray warp-ins of Protoss' dark templars can be very strong, since dark templars are pretty good at sniping missile turrets. Ridiculously-late-game, Terran ghosts win again, with the ability to "harass" with nuclear launches and snipe. Again, you largely limited by your ability to control the units (and also mana, but ridiculously-late-game you would have plenty of ghosts gathering mana).

Speed harassment

Terrans win at first with the reaper, then the oracle wins in the mid-game. After that, boosted medivacs are a stronger speed harassment, and then large backdoored warp-ins are probably stronger (but more expensive).

Range harassment

Mainly for bad maps, but those do happen ;-). Siege tanks on cliffs, tempests on easily-guarded or unpassable terrain...siege tanks are earlier.

Conclusion

Terran seems to get first strike at harassing a Protoss with most categories, except that the oracle is a harassment champ. By the mid game, almost all of us mere mortals are limited by ability to multi-task, rather than racial abilities.

In the super-late-game, largely as theory-craft, you can weigh the relative strengths of Protoss' large warp-ins (including cloaked dt's and sentries that can block off ramps) and oracle vision+worker deathrays vs Terran's high-dps bio strike teams (with long-range sieged tanks in medivacs!), nukes, cloaked banshees. And perhaps you can weigh battlecruiser warp-drive "harass" against carriers dropping off their interceptors ;-). However, that's probably deviating far from the question of "harassment".

Additional factors

• I left out Protoss Adepts because although their ghost image could be considered somewhere between a time-shifted blink and speed harass, it's not really "the best" at speed harass anyway (and blink is included in cliff harass). They're more of a good all-around unit with good micro tactics. I suppose blink and psionic transfer could be a whole other category of "exploit-that-your-shields-regenerate" harass, equally viable at the front door as well as a flank or run-by, similar to a medivac healing but with less cost and control required.
• Harass defense: Protoss' photon overcharge allows for a limited amount of very-flexible defense for the cost of the mothership core (a useful unit anyway) and some control + attention. Terrans have to pay for their harass defense, either with units + control + attention, or minerals (bunkers, turrets).

I somewhat disagree from @chaqke answer. I'll explain why.

[1] What I wish to know is, what method is used to balance StarCraft with respect to Protoss' ability to do aggression and harass?

Sc2 gets some new balance patches when the state of the game seems to favor one or another race. Speaking about the latest notes released by David Kim and his team, Protoss' Adepts seem to be too strong in early game vs Terran.

So, since everybody reported that thing happening, adepts will be most likely nerfed in the next patches.

[2] Is it objectively true that a Protoss can't be as good at aggression and harass compared to a Terran?

In my opinion, no, absolutely not. At the current state of TvP, Protoss has huge harassment power.

Protoss:

• Opening with Adepts -> Scouting, Get rid off Reapers, Forcing Terran to Bunker Up, Protoss has map control, Upgrading Adepts and drop them with 4/5 gates
• Opening with Oracles -> You can punish greedy opponents and block the first pushes
• Opening with Phoenixes -> Protoss has map control, Terran drops denied, Forcing Terran to build turrets/WidowMines/Cyclones, denying Liberator Harass
• Other non popular openings: Based on DT drops or similar, not really early

Terran:

• Reaper opening -> Scouting, getting maybe 1 probe, killed by an adept or Pylon Overcharge
• Cyclone opening -> Map control, killed by Blink Stalkers or Phoenixes
• Widow Mine Drop -> If no robo opening and no Phoenixes opening it's very good, in the other cases its basically a lost game
• Banshee opening -> Way too easy to scout for Protoss, probably getting killed by Phoenixes or a well placed Pylon Overcharge
• Liberator Opening -> Pretty cost effective, maybe getting 4/5 probe kills
• Fast bio drop -> Gets killed by Adepts, Pylon Overcharge or Similar
• Fast Tank + Bio Drop -> Pretty cost effective, gets killed by Phoenixes openings or good Toss Micro

So, basically, if Protoss opens with 1 or more Adepts and Stargate it's pretty safe and also can make a mid game all'in or attack focused on Adept/ChargeZealots Warp Prism drop (Very popular).

[3] Is it merely that most Protoss prefer to play defense, and simply haven't explored other aspects?

I don't think so, if you watch high level korean players, they already know how to harass in early-mid game. You can also play defensive, but playing a bit aggressive, if well done, always pays off.

[4] For two equally skilled pro league players, one Protoss and one Terran, would the Protoss always perform worse than the Terran using aggression/harass tactic?

Absolutely not. It depends on the skill of the players involved in that game. But, for the actual state of the game, I would put my bet on a better Protoss' harass.

[5] Could there possibly exist a pro league Protoss who plays an aggressive/harassment Terran-like style and still do well enough to win tournaments?

I can name Parting, CJherO and Zest. Of course, the harassment is done differently from Terran's harassment but these guys know how to poke their opponent for sure. MC is not playing tournaments anymore, but he's also capable of doing that.

In Conclusion

In my opinion, by now Protoss is winning on that aspect on Terran, I'm an experienced Master Protoss but it's still my personal opinion. If you want to get started with some serious harass, take note of what I written over and watch some serious Protoss Streamers that stream often:

• Boss Toss - MC
• Mana
• State
• Parting
• Patience
• King of Drama - Naniwa
• GSL/SSL/PROLEAGUE/WCS/DREAMHACK

Now, in response to @chaqke opinion

Cliff Harass

I somewhat agree. Ok, speaking about TvP, the reaper is the fastest unit in early game. But at the current state of the game, Protoss is way too far better than terran because of adepts. Every Protoss is opening with adepts. They are strong vs bio and they can chase reapers easy and kill them with few Shots. If you want to get rid of Adepts you can:

• Build a bunker and a barrier -> Protoss has map control
• Go for Cyclones -> Not really ideal against most of Protoss' units

So, In my opinion, Protoss is way better in early game.

Drop harass

I agree but mid game all'ins with prism (Charge Zealots and Adepts) are very strong and easy to do.

Air harass

I agree but in my opinion Oracle is a really powerful tool. Phoenixes are really a thing in the current meta. They allow you to repel most of the early pressure, harassing, forcing wrong units and taking map control.

Cloak harassment

I agree.

Speed harassment

I somewhat agree. As explained before, reaper can be fast, yes, but adept really counters it properly. Speed is an important thing, yes, like boosting your medivacs or just stimming some bio into far away opponent's bases. But, maybe Charge Zealots, Adepts and DTS are not that fast, but they can harass in a really cost effective way and you don't need to pay as much attention on them as the Terran does with its drop.

Range harassment

I agree, but you have also to mention Disruptor and Oracle Revelation for Protoss. Revelation gives both Disruptors and Tempests a really powerful harassing/attacking power.

I hope I've been helpful, GL & HF.