I was raised in Jackson and worked in Yellowstone a stint as well. 4 nights is not a lot of time in Yellowstone, and only really gives you time to hit the main tourist locations, which won't necessarily give you the best chance for wildlife, or getting away from people and seeing what it is really about. It really depends on your agenda and I don't know your setup, but moving your rig in the middle of a trip takes a bit of time and almost always severely impacts recreation time for that day. Typically you will try to come home a little early to prep, or spend the morning prepping for the move, only to move and check in during "check in time" (though FB can have openings if early). Then you take a small/close trip to close out the day. Before you know it, a day is gone. At the same time, you know your detail better than I, so...
You likely know this, but Madison is a bit nicer in that it's more of the true camping experience with more space, fire pits/no hookups. You do however share with tent campers and generators which can tend to be noisy, especially with the West End traffic. But, you can easily spend 2 full days here between OF, the geyser basins and Firehole area. Mammoth will be a quick trip you would want to do from here as well and can be fit in one of these days. As for traffic, early morning traffic is MUCH better, so adding on another 10 miles or so by staying in Madison to see the main site of the day is not a big deal. Driving an RV during check in time is.
FB as you likely know is an over glamorized parking lot and you are up close and personal with your neighbors. Full hookups, but no fire pits, tables, etc. This is a hotel room. I am staying there 4 nights this year as well, but I will be there just to sleep and not looking for that "camping" experience. Anyway, if you are attempting to see wolves or grizzlies, this might be better as you are right in the thick of it at FB, but also closer to a better chance in Lamar. If you hit Lamar preferably very early, but late works as well (bring a spotting scope or bino's), you can also spend the remainder of the day in Canyon to see the Upper/Lower falls from different vantage points including the Grand Canyon. Definitely the most impressive waterfalls in the park that is a must see, but many others are beautiful as well.
BTW, not sure what your other plans are, or what entrance you are coming in, but you might consider taking that extra night (or two), and hit Teton National Park. The route through this entrance is your best chance for Moose as well, and while Yellowstone is magical in many ways, the Tetons will also give you just a bit more; especially if you do some hiking around Jenny or Jackson Lake.
So, my final answer is whatever works for you and whatever will meet your agenda. Both sites are central to the park and will afford similar benefits, though picking one and driving the extra mileage is doable if you travel early/late. In my view it is likely a better option than splitting up the trip, again because moving does take quite a bit of time especially in you don't know how long you will wait just to check in to FB. If you were staying longer, then maybe this would be a great option, but as it stands you only have 3 full days...
And sorry guys, I am not a yellow bus tours kind of guy. While they will give you a bit of history, and hit the main spots, they do so at the busiest times and on a schedule, so you are either forced to wait for others, or move faster. There is so much info available on Yellowstone, even documentaries, you can easily get the history before you arrive allowing you to cater your visit to what you want. Now if you are going in blind, without the desire to research or set a plan, and instead let someone else do it, then a bus tour is a good option. While you might say it's not an option for me because I lived there, it is the same for me anywhere. I just won't do the over the top touristy tours unless there is little choice and I have just a couple days in a strange area. It's inefficient and typically very general. Just my $.02...