Manchester velodrome has tire recommendations obviously based on what sticks and what doesn't:http://www.nationalcyclingcentre.com/tr ... ification/
It sounds like tread compound is more crucial than tread pattern, for wood anyway.
That's correct. We don't have too many of them any longer, but there used to be lots of tires with yellow or red tread, or tires with a very narrow black center tread and colored sidewalls that went almost to the centerline. Those rubbers tend to harden and don't grip as well even when fresh, so you're prone to slipping with them if riding slow on the bankings. Similarly, smaller tires (which used to be the norm) make you prone to slipping. And whatever tire you use, scuff the surface with sandpaper or by riding around the apron for a while, and always clean the tire off with vinegar or rubbing alcohol (I prefer the latter). If you've never ridden a wooden track, there's a lot of very fine wood fuzz that sticks to the rubber of your tires, making them slippery. There's generally a lot of dust on some tracks, which tends to do the same. It pays to clean your tires constantly -- the alcohol will evaporate and dry very quickly and if you spray some 90% Isopropyl alcohol (versus 70%, which is rubbing isopropyl alcohol) and then wipe the tire off with a towel, you'll have fewer problems with slipping or with punctures.
As I indicated above, the general view is to use a smooth tread on wood tracks and textured tread on concrete, but it's really questionable whether there's a difference between them. Track riding is as prone to voodoo and myths as any other kind of cycling.