Can't restore iphone, iphone doesn't have enough space

Hi guys,

I did a full a back up of my phone this morning because I needed to exchange it for a new one (dust spots between the back plate and the camera).

I got the new phone, came home to restore from back up and it wouldn't let me. Said that there is not enough space on the iphone which seems weird.

Anyone know how I can restore?

I did a search term on the forum but it didn't generate the right threads.

Thanks!