Both arguments seem to have valid points however I think the only real difference is tire pressure and width. Even on a dirt road I notice no difference between light treaded Marathons and Marathon Slicks. But 85 psi 35mm tires definately have better traction than 120 psi 25mm. You best bet for wet weather traction is probably something like a Schwalbe Big Apple (50 mm or 60mm) run under 60 psi. Probably wouldn't be terribly slow either but you will need a MTB or 29er to be able to fit the tires with fenders (or even fit the tires period).
In wet conditions TDF racers still use slicks but will run wider tires at lower pressures than they use on dry days.
Craig