Which Hector will be most effective with a Distant Counter/Vantage build?
While this ultimately will fall to your own judgment, there are objective pros and cons to each Hector:
Your -ATK/+SPD Hector is missing out on one of his best stats, which makes Hector the monster that he is. Speed is definitely Hector's least useful stat, as he will almost always be doubled by enemies. However, due to the fact that this was the first Hector you summoned, he has the advantage in the skills he's inherited.
Your second Hector, the one with the +DEF/-RES, would make a much better unit. Even though his attack isn't increased, at least it isn't being harmed by his boon/bane spread. While it may take a bit longer, you'd ultimately find the most success with this Hector.
Personally, for checking the viability of heroes, I look at their Gamepress page. Here is Hector's. The most useful stats for a boon on Hector are Attack or Defense, while the least useful stat (that is, the one that will do the least harm to have a penalty in) is Speed.
The build you're using is one of the "best" Hector builds, using a combination of his default Distant Counter with an inherited Vantage 3. With this build and a Defense boon, once Hector falls under 75% HP and activates Vantage, he will be able to strike anyone who attacks him first for 52 base damage and then tank any physical attacks with a whopping 40 Defense (more or less, depending on buffs/debuffs). These numbers are using your second Hector. Your first Hector would only hit for 49 base damage, which can most definitely be a game-changing difference.
However, the important thing to notice in both cases is that Hector only attacks once. Even with a Speed boon, Hector will only reach 28 Speed. He would need to be fighting an opponent with no more than 23 Speed to score a double.
From this list of Heroes, the only heroes who would be doubled by Hector (this is assuming they do not also have a Speed boon) are Zephiel, Sophia, Berkut, Effie, Hawkeye, Henry, Leo, Lukas, Beruka, Reinhardt, Adult Tiki, and Wrys. For reference, even with a Speed boon, Hector will only be able to double 12 of the 168 currently available heroes. On the flip side, a 28 Speed Hector still suffers double attacks from 70 of the 168 heroes, again assuming a neutral Speed nature. Assuming a Speed boon on the opponent, this number rises to 108.
An alternative solution to this would be to simply merge your old Hector into the new Hector. From personal experience, merging a hero with inherited skills into a hero with a blank slate of skills will unlock all skills the merged hero had unlocked. Your first Hector had Vantage 3 learned and equipped? Your Level 1+1 Hector now knows Vantage 1, 2, and 3.