I watched the 80's shows and movies and had several of the toys, and so I'm obviously biased as far as liking the franchise, and I'm really happy to have a modern version of the show that my kids like as well.
The setting and characters are all quite consistent with the originals, but it is a new storyline: Instead of the Care Bears coming to Earth to rescue human children, the Care Bears explore a new territory in their own world called "the Silver Lining". They find all kinds of new non-Care-Bear creatures to save by helping them with their feelings and interpersonal relationships, very much like they did with human children in the originals.
It's true that there are no Care Bear Cousins. And the cast is generally much smaller than had been built up by the end of the 80's shows. It's more similar to the original start of the series when there were only a few bears that the show focused on. (I think there were 10 original bears in the 80's series, and this new show focuses on just 5 of them.) The other bears still exist, and pop up from time to time, but they mostly stay in Care-A-Lot while this team of 5 bears explores the new territories.
The villains are no where near as evil as the villains in the old shows. This show keeps the evil at the level of bullying, rather than kidnapping and attempted murder that we saw from some of the 80's villains. You can decide if that's a good thing or a bad thing, but in my opinion the new show is much more age-appropriate for small children. It does still give some opportunities for redemption of some of the villains, which was a theme that existed for some of the 80's villains, but these new villains are a little easier to root for when they start flirting with turning good.
The Care Bears themselves have some deeper character development as well, particularly Cheer Bear---who deals with some self-esteem issues while learning to lead the small team---and Grumpy Bear---who is still grumpy but also caring, unlike some of the older shows that portrayed him in a mean light, this new show does a nice job of letting him accept his unhappy feelings without vilifying him for them.
Also like the original 80's show, they do a great job of spanning gender lines. My sons love this show and don't think of it at all like a girl's show, just like it never occurred to me or my brother back in the 80's.
All in all, I think it's a beautiful show, and I really hope they keep making more of it. Give it a shot.