A good driver should do all of them well, so you can pick to suit the program.
BTW, the choice is not between WDM or ASIO, but between MME or ASIO. If you want to run Tascams GigaStudio/GigaSampler you also need a driver that handles the GSIF interface too.
E-mu and Digidesign seem to have made ASIO drivers with a limited MME interface tacked on, while M-audio have WDM drivers with MME, ASIO and GSIF etc built in. There is no evidence I know of to suggest that a WDM drivers ASIO has to be inferior to a seperate ASIO only driver.
For the manufacturer, a good WDM driver would appear to be no easy thing to make. WDM (Windows Driver Model) is a recent driver standard from Microsoft, and judging by the problems some manufacturers have had, the documentation they have to work from can't be all that good! Much easier I would think to go for an ASIO only design, which has nothing to do with working with Windows sound system.
As of this moment, the lowest latency is no longer limited by the driver, but the way a pc works. A sound driver DMA buffer of 64 samples gives about 1.5ms delay at 44.1Khz and is as fast as the system will comfortably allow. As far as I know, both standalone ASIO drivers and WDM/ASIO ones can reach this limit in a well optimised machine.
You should certainly obtain a card with at least a good ASIO performance. But if some of your programs cannot use ASIO, a card that has poor or limited MME or no GSIF will be a waste of money for you - especially since there are cards now that do all of them well!