The XT version of the HD7870 is more properly a cut-down HD7950, so it would be the faster card. Your PSU can handle it; can your case handle the added heat? If not, the HIS HD7870 (if it has their Black Hole cooler) will exhaust its heat from your case.
Either card should outperform the GTX660. If you plan at some point to run two cards though, get the GTX because Crossfire has problems that SLI does not, according to the FCAT tests now being done. All of them are competent for 1920x1080 gaming.