Most of the arguements that people make for aspirin state that aspirin extends the thermogenic effects of ephedrine by inhibiting the enzyme cyclooxygenase and therefore decreasing prostaglandin synthesis (why aspirin is an anti-inflammatory). This helps combat one of ephedrine's effects. Ephedrine stimulates the release of norepinephrine, which stimulates the release of adenosine and the synthesis of prostaglandins by the activated tissue. Since aspirin inhibits the synthesis of prostaglandins (1), it is believed it enhances the effect of norepinephrine (the reason why caffeine is included in the stack to combat adenosine). By increasing the amount of norepinephrine one would expect to increase lipolysis. Caffeine achieves this, however in actual studies aspirin as yet to prove the same. One can only hypothesize on why aspirin's effect on prostaglandins does not effect lipolysis.
There have been no studies that I am aware of that show that an ECA stack is more effective than an EC stack. The only studies that have been proven to work are when an ECA stack has been done in a study against a placebo. Couple this information with the effects aspirin has on the stomach (nausea, heartburn, and sometimes bleeding ulcers) one could conclude that the most effective stack would be just Ephedrine and Caffeine.
1. Rawson ES, Clarkson PA. Ephedrine as an ergogenic aid. Performance-enhancing Substances in Sport and Exercise. ED Bahrke MS, Yesalis CE. Human Kinetics. 2002.