We've been to Rimini twice (7 nts and 5 nts). On both visits we popped into Cattolica also.
Personally I think both are nice, but I'd still go back to Rimini, and take the bus into Cattolica for a visit. Rimini has an old town, more shops (non touristy ones in the old town) and has some tourist attractions too.
On our first visit we stayed at hotel metropole. It's a 3* with small pool, although it was too cold to use when we were there (poor weather). To be honest we liked the beach anyway, as it was so well maintained. Hotel basic, but ok, and at the time (not sure about now) there was a scottish receptionist who was excellent for local info. Also our favourite restaurant nearby (Joe's pizzeria).
http://www.hotelmetropole.it I think.
Next visit Hotel Mercure La Gradisca, which we didn't like. Location was excellent (nearer to train station than hotel metropole), but the room wasn't so good, small and badly finished and supposed to be 4*. We had a successful complaint with the hotel chain and had a most pleasant stay in Rome for our troubles.
I don't have a clue what the hotels are like in Cattolica. A lot look small/basic etc. I'm sure there should be some better ones.
If you want something more 4* in Rimini, the hotel Le Meridien (the chain) looks good. It has some nice shops underneath too.