Well actually, Attack on Titan is a mahou shoujo vampire anime. The real mecha shows in disguise are Kill la Kill and Nanoha

Anyway, as for the topic at hand

The super robot vs real robot question has no straight answer for me. Overall, I enjoy real robot series more because super robot series tend to be "monster of the week" type things that go nowhere for a dozen episodes at a time. However, I'll take the peak highs of super robot series over the peak highs of real robot series any day. This is why my absolute favorite mecha series are super robot series that reach those peak highs without also falling to the "monster of the week" formula too much. Things like Gunbuster, GaoGaiGar FINAL and Gurren Lagann. (all starting with a G which is amusing but pure coincidence)

Favorite robot is honestly impossible to say, there are so many amazing ones out there that i can't rank them. But I'll give a shout-out to the Dynamic General Guardian line of robots from Super Robot Wars:
Dygenguard.png DaiRaiOh.png

As for recommendations, beyond what others have already mentioned, obvious stuff like Gundam/Macross and Go Nagai's works (Mazinger, Getter being the two major ones, but he also made things like Grendizer and Jeeg) and my favorites in this post: Suisei no Gargantia, Sousei no Aquarion, Patlabor, Diebuster (sequel to Gunbuster), Full Metal Panic, RahXephon, Fafner (gotta get over a lot of angst for this one though), Dunbine...and honestly many others but I'll leave it at that

Except one more thing, on the game side of things: If you're into giant robots and not entirely opposed to tactical RPGs, you owe it to yourself to at least check out the Super Robot Wars series. Most of them are cross-over games featuring a bunch of mecha series, while the Original Generation games take all the original storylines/characters from those cross-over games and combine them into a new original universe. If the former appeals to you more, officially translated entries include SRW V, T and X, but you can also grab fan translations of entries like Alpha Gaiden (PS1), or A Portable (PSP), among others. If the latter appeals to you more, Original Generation 1 and 2 on the GBA were officially localized, while Original Generations, a PS2 remake combining those two GBA games, is fan translated.