you'll find that the 3 phase machines are full industrial units and therefore beefier. as to what is better, there is probably little difference in the same model machine that offers 3 or single phase options. The main diference would be the transformer. Its just harder to get 3 phase if you're not based in an industrial unit so offering both solutions makes sense for the manufacturer.
I don't know about performance difference but if you go for 1ph then at lower power settings it will run on a 13a supply(with a suitable fly lead adapter) which may be useful