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.
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.