In my opinion, that new Sonic Boom design actually succeeds in making the design of Modern Sonic look even less appealing than it actually did (even if the fans always complained about that design too). The whole "green eyes" thing hardly seems like a big deal now compared to having stupid white tape all over his body.
Honestly I'm not sure why most people don't like the redesigns, there not to bad. Although I'm gonna have to get used to seeing knuckles. It's probably because I'm not afraid of change unlike most people.
You're right on that. Sonic's got the bandana and the long legs because he's the runner and the most adventurous of the team and Tails has the toolbelt and goggles because he's the brains, the smart kid and the Sonic Team's Mr. Fixit. Knuckles is so buff because he's the strongman and the heavy hitter, but he's not as bright as the rest might be. Amy's look shows how she can keep up with the others and prove that even a girl like her can be badass when it comes to fighting evil. And Sticks, well, she's the wild girl who proves to be much more primitive than the other four (i.e. not wearing gloves).
I like the fact that characters like Sonic and Knuckles are shown aging or maturing (in body size at least). As seen with this picture, Sonic started out as a small kid and now he looks like a young adult. Knuckles is looking more like the big tough warrior he acts like. Even though other males characters in Sonic have different skin and hair style... they pretty much have the same body design... it's time to change that.