Is there a reason I seem to see more Dominixes then any other T1 Battleship?

I strongly recommend the "Know your enemy" series from Azual Skoll, it's the best overview over the capabilities of nearly any ship in EVE. If you want to know more about a specific ship and how it is usually fitted and flown, I'd look there first.

Now, the Dominix is the drone boat, this makes it for example very good at running missions AFK because drones switch their targets automatically. If you're mostly in highsec, you're probably watching mission runners.

But it really depends on where exactly you are, in lowsec you don't find many battleships usually, they're just too vulnerable alone. For big fleets the Amarr battleships are generally regarded as very good. Minmatar is often considered the best solo and small gang PvP race, but I see their battleships not very often.

The Scorpion is an ECM ship, as a battleship its pretty vulnerable and you will find the Falcon (Caldari Recon ship) far more often as the ECM ship due to its covert ops cloak. The Typhoon has a split weapon system, it's very skill-intensive and torpedoes are problematic in PvP due to the low range and the ineffectiveness against smaller targets.

Dominix's are a great drone ship and cheap compared to other drone-focused battleships.

If you have great drone skills then the Dominix will be better for you than some, but not "in some massive way". Most of the combat ships in the game seem relatively balanced, such that if you master the skills that ship focuses on and fit the ship accordingly, then you should be able to hold your own, relatively speaking.

Ultimately, whether a particular ship is good or bad for you depends on your skills and your budget.