I realized that I was running Ati Catalyst driver version 5.5 (released a year ago) so I updated them to the latest 6.5. And now, both MBT and WW2 work! I can see none of the problems I encountered earlier.
Thank you Andy for your help. I am so sorry I caused you any extra trouble. I really should have tried updating my drivers a bit earlier
Anybody suffering from a laggy gameplay in WinSPMBT or WinSPWW2: if you have an Ati Radeon card, make sure you are running the latest Catalyst drivers.