I think the notion used to be that RWD mowers were harder on the grass because if left engaged, and without any differential action, one wheel would always slide against the ground (usually the inside wheel would spin faster). FWD mowers, as stated earlier, can be left engaged when pivoting for a turn.
I have owned both, and both were equally reliable for me. I do prefer RWD, especially when bagging, because FWD didn't tend to keep a straight line across the lawn...it would tend to wander left/right without correction. The RWD mowers seem more direction-stable.
I do agree with the comment that a RWD Lawn-Boy is about as close to mowing perfection that you can get. My 8157 model is a very early version of the Easy Stride concept, and you push the near-vertical mower handle to get it moving. The handle is pivoted about halfway up, and as you push the top of the handle, it pulls on the drive cable. The harder you push, the faster the mower goes. You still get a decent amount of exercise because you have to truly walk the yard. With many types of drives, you can easily let the mower "pull you along".