I've watched both the US and UK performances. Definitely live on the US show. The verses at least. Some off notes and the one guy, Louie, sounded bloody awful (how did he get into the band?!!) For the chorus I think they were all singing live over a pre-recorded backing track but the verses were definitely live. I'm not a fan but I'll give them it was a decent vocal performance from 3 of the group!
On the UK show the whole thing sounded mimed to me but of course I'm not 100% on that. They sounded far more note perfect and polished to me. Even Louie sounded almost in tune!
In the US I doubt they'd have mimed the whole thing anyway as lipsynching on live tv seems to be frowned upon a whole lot more there (Ashley Simpson's mishap on SNL being a prime example) but here more acts seem to mime on tv and have done for decades (ever seen the 60's pop show Ready Steady Go? All mimed!). A lot of acts today of course sing live but with pre-recorded backing vocals, we all know that. Even great singers like Beyonce and Mariah do that! If they're singing all the main parts of the song live it doesn't bother me much if they have pre-recorded backing vocals accompanying them, especially if they're dancing around like crazy (who wants to hear a wobbly, out of breath vocal?!). But in the case of One Direction there isn't really any excuse for miming as they don't dance, they just stand there looking bored stiff!!
Anyway, definitely live on US XFactor (Louie would never have mimed to such an abysmal vocal, lol!) and the others sounded a little wobbly in places but (to me anyway) they sounded mimed on the UK show. But who knows, eh?! All I know is that Louie and the Irish guy are damn lucky to be in the group with such weak voices!