For anime, I honestly don't really know which one I'd consider my favourite. I've watched so many animes that I thought were good, like FMA:B, Attack on Titan, Fairy Tail, Naruto (as overrated as it is), Code Geass, and the list goes on. I also really liked the first half of Sword Art Online, but I reckon most people know that it lost its touch during the ALFheim part. But to choose a favourite between all of those.. I honestly don't really know which one I'd pick. I reckon the two that's be closest to the top would be FMA:B and AoT. FMA:B is really good at tinkering with your emotions as well as providing you with lots of good laughs, and it just had an overall great plot and premise. I haven't watched it in quite a while, but I don't recall it to have too many fight scenes, at least not compared to Attack on Titan, but the characters were memorable and lovable, and I definitely feel like it's one of the best to date. Attack on Titan on the other hand was more about the action scenes, and the intensity and suspense they encompassed. Contrary to FMA:B, while some of the characters were kinda memorable, I don't think many of them really got a chance to shine. I mean of course it isn't finished yet, but so far it has mainly been Erin, Mikasa and Armin, where we really got to know the Recon Corps members in some of the latter episodes as well, but I didn't feel like they ever really elaborated too much on all of the other graduates. Hopefully we'll get to see that later on, granted it gets a second season. But for what it's been so far, it's definitely at the top of my list.
As for mangas; I've never really been too big of a manga reader. I read a bit of Naruto, since I have a friend who used to be really into it at one point, and he convinced me to read some of it, but I'd already watched some of the anime, and had grown quite accustomed to that over the manga. So yeah, not really a competitor. To be honest, the only mangas I recall reading completely through are the Dragon Ball manga and Gantz, both which I've thought were just amazing. Dragonball probably takes the spot as my favourite entirely due to nostalgia, and also due to how half-arsed the ending of Gantz was, but just the whole premise of Gantz, the whole alien hunting thing, it was just a great concept, it was very well issued, and I really enjoyed all of the missions, and I feel like the ending just didn't capture the essence of all that quite as well. Because it set a completely different atmosphere. And I feel like that kinda drags it a bit down on the rating list. That and all the fan-service. In any case, it was still a great manga, and I wish it would've been longer.