What are the advantages to larger rear wheels or front drive on a push mower?

The larger diameter of the bigger wheels makes it easier for them to roll over any imperfections rather than butting up against a bump or dropping into a slight depression. On anything other than a perfectly smooth level surface that will make the mower easier to push and it will make them easier to turn. Larger rear wheels are also less likely to be pushed off line by any surface irregularities so they tend to take less correction from the operator to stay on a straight line, which makes it even easier to mow.

There is only so big the front wheels can be without limiting the ability to cut close to edges so you seldom see designs with large front wheels.

Adding drive to the rear would be helpful if you did have hills since rear wheel drive tends to provide more traction than a front drive system on a mower. But with the drive at the mid-point of you and the mower, as it is on a rear drive mower, it makes it more difficult to turn than with the drive at the front.

So, since you don’t have hills to deal with, a front drive with large rear wheels would be a good combination to reduce your effort and still maintain a lot of easy maneuverability.