I've bowled just as well on the right conditions with asymmetrical equipment as I have with symmetrical equipment. Depends on the match ups that I see with the lane conditions, lane surface and what the operator of the bowling ball can do. There have been times when I've bowled out of state tournaments where I bowl in different houses for different events- one house I may need to use a symmetrical, early rolling ball, another house I may need an asymmetrical skid/flip type look to the lanes.
I think these days you need to know your equipment and how it will react on different lane conditions/surfaces so that you can make the right decision quicker than ever if you want to stay near the head of the pack. I have some equipment that can work well in a variety of houses (Diablo, Absolute Inferno, Havoc) and then I have other pieces that are condition specific (Slash, VP2).
Matt