Two types of tile cutter I see widely used, the "table saw" type with
a diamond wheel and the tile slid through it (or the wheel slides over
the tile), - or the score-and-crack type.

Which would work best for large porcelain tiles (600mm by 600mm, about
8mm thick)?

I borrowed a friends table saw type (which is too small for these
tiles - but allowed me to at least try taking a slice off one edge) -
and it cuts them, smoothly but very slowly.

So do I need to get a hold of a larger/professional model, or is score-
and-crack better on porcelain?

I also need to do an irregularly shaped cut-out on a tile or two to
fit around a shower valve.

What is going to work well for porcelain tiles for irregular cut-outs?