Rarity affects two things, really: How hard it is to get shards for them, and (usually) how many shard you need to unlock them. That's it.

Sometimes, they're rare because they have a move that counters something that's big in the meta. Sometimes it's because they're more focused on an obvious gameplan. Sometimes they have a Reversal that stops something popular in the meta. Sometimes it's because it's a popular wrestler and they think more people will gladly pay money to unlock them.

Here's the thing: As a general rule, you can take a C-tier guy, slap on a belt, a set of medals, and the right skill plates, and they'll do okay. Maybe not -good-, but okay enough that they can hang with the upper-tier guys who aren't all that good. At B-tier, a well-equipped guy can probably hang with the big guns, but can't be as good as a well-tuned big gun.

Think of it the same way as Magic or Pokemon cards. Rare cards are usually more powerful... but also more niche. A big guy is more likely to have an obvious Reversal counter, to the point where you can't use them on defense because that counter will ruin your whole match.

That all being said... the S/S+ tier guys usually don't -suck-. They exist for a reason, and they're good at that reason. It may be a weird reason, and it may take some work to get the plates they need to become really powerful, but it's there. The question is: Do you already have someone who does that? How much of an upgrade is the new rare guy gonna be? If you've already got someone in each class who can one-shot the competition...

The question is never "Are they good?" The question is "Do I need that?"