Not at all. All you get is the Legend rank for medal collecting.
The medal system was a good idea, giving players some reward to do what they usually do in B2/W2, either just playing the game or whatever their post-game plans are.
For me, the medal system has its good parts and bad parts. I do like seeing the medal man in the Pokemon Center whenever I go in there, and I talk to him to see what new reward I can get. Since I'm not actively trying to get any medals, it's always a surprise to me what I get. The bad part about it is that I know I'm not going to get all the medals, since there's only two other people that I know of that play B2/W2, and that's not enough to get any medals. Once I realized it wasn't even conceivable for me to get all the medals, I gave up on my quest to get the ones involving the Dream World.
There's not really a medal that I really like. Scanning the list, I will say that "Good Night" is an adorable medal. The fact that it's a nice shade of pink and is from doing something rather cute makes me smile.
I liked getting the medals. It was a fun side project. I was really disappointed with the "ceremony" for when you got 50 medals. The comic describes how I felt perfectly. I have kind of stopped going after the medals because there are just too many.
Not directly. But if you have a lot of medals, you've most likely have met the requirements to upgrade your trainer card. It's basically a prestige thing. The higher your rank, the more stars you have next to your trainer profile online, and some NPCs have different dialogue (most notably Nurse Joy because she almost instantly heals your Pokemon). Medals and Hint Medals just basically guide you to that. But if you don't care about prestige, theres no reward I guess.
Personally, I don't have any friends to do Funfest missions with, so I can't get all of the medals (at 203 currently) which is kinda lame. :/ That means I also can't get the Black trainer card.