the HD 7870 is a bit better than the gtx 570 but I'll be playing on a 1080p (1920x1080) and their performance is kinda the same at that resolution.
the gtx 570 is 50€ cheaper too!
The preformace of the 7870 is going to be smother than the 570, even at 1920x1080. This isn't a big deal for older games, but newer ones are going to be quite a bit nicer with the 7870. The 7850 is the card that's more comparable with the 570.
worth 50€ more?
EDIT And if I buy a Hd 7870, which one is the best?
If you have the money and it isn't going to hurt your rent or anything I'd say it is. I'd look around at a couple of sites though, in Canada (and I guess the US too) the two cards are only about $35-$40 more for the 7870.