Or does it just look very similar?

Think it's very similar as pretty sure the X Factor one is much wider?

Bgt stage - http://i3.mirror.co.uk/incoming/arti...%202012-821995
X factor stage- https://upload.wikimedia.org/wikiped...olandStage.jpg

I think it's the same studio they'll just build the stage slightly differently for the two shows.

gcmac is right, it's the same sound stage, but it's two different sets put in there and taken out each time. They film some other shows there too, it's Fountain Studios in Wembley.

For some reason the BGT set looks emptier even if it's the same studio...