Hi Ben,
Whilst in principle both flavours of lathe spin stuff to allow it to be cut round there are pretty fundamental differences between metalworking and woodworking lathes.
Metalworking lathes in general turn more slowly and are engineered for small precise cuts with adjustable tailstocks saddles and compounds etc. On the other hand woodworking lathes will tend to turn more quickly and be less precise - their tailstocks have no adjustment and the saddle and cross-slide are replaced with an easily and quickly adjustable banjo and toolrest.
In short, they've evolved into quite different animals over the years.
It's quite possible to turn wood on a metal lathe and vice versa but for maximum enjoyment and efficiency I think that you'll find that sticking to the material each was designed for is "best".
HTH
Jon