I lived in Tahoe for 6 years, and skied Squaw. Now I live in socal, and ski Mammoth 3 weekends a month, from mid-Nov until May.
I love Mammoth, but I don't see it beating Squaw. Mammoth has great terrain, don't get me wrong, I am lucky to ski it. There is lots of great stuff in the TOTW, P4/Philippe's/Kiwi area, head chutes, Hangers/Varmits/MJB's......I actually think Mammoth's steeps are very underrated. But there is no way it beats Squaw. Squaw has FAR more steep terrain, and has a better variety of steep terrain. Squaw is also a more featured mountain, with many more cliffs to jump off. Mammoth has a longer season, but Squaw always went to Memorial Day when I lived there, even in the normal years. Both mountains get lots of snow, and it is of the sticky variety, meaning good coverage on the steeps.
One of the occasional problems with Mammoth is that the wind can turn a blower pow day up high into a windbuff day. It is still sick, but not quite what you want. I have gotten plenty of blower pow days on the top at Mammoth, but the wind can ruin things. I saw fewer days when the wind packed the upper mountain at Squaw, more days where you got the top in pow.
The wind at Mammoth can also be good. It can smooth things over well, and keep you skiing nice, buffed out steeps for weeks after a storm. Mammoth's wind is definitely both a blessing and a curse.
Having said that, there are some storms that come in as rain for Squaw, and snow for Mammoth, due to the elevation.
I ski Mammoth because driving 11 hours combined 3 weekends a month is doable. Driving the 17-18 hours combined 3 weekends a month, which is what it takes to get to Tahoe from socal, is not. If I were given a choice of whether to ski Mammoth or Squaw, all other things being equal, I would choose Squaw in a second. I love Mammoth, but I really miss the mountain at Squaw. As great as Mammoth is, Squaw is better for non-park rats.
There are other things to consider though: I prefer Squaw for storm day skiing. You can lap Red Dog, KT, and Squaw Creek, and got tons of pow in the trees. You can also go into the enchanted forest. I love Mammoth storm days, but it is mostly chairs 22 and 25, so I would rather ski Squaw on those days. Having said that, I have heard that the low Squaw pass prices have really changed things, making big lines on storm days.
Overall, all other things being equal, I would choose Squaw over Mammoth skiing wise. I still love Mammoth, but Squaw just has better terrain. I like Squaw better on pow days. If I were going to quit my job, and ski bum again, I would choose Tahoe/Squaw in a heartbeat.
I don't have Jackson beta, but everyone knows it's a sick mountain.
As others have mentioned, Mammoth Lakes does have a very good bus transit system. You can get away without a car there.