I can't compare the two; I haven't played the P-lyte. But I can vouch for the Aerodyne! That bass has a great neck and feel, it's light, it sounds good with the stock pickups. It is really comfortable to play. Looks are in the eye and all, but I think the Aerodyne is a gorgeous bass. I like the other colors available in the Japan market, but the black ones they make for export to the US are dead sexy!
During the pandemic, I've been playing a little bit more often but rarely for more than an hour 2-4 times a week. Then we had our first practice in 4 months last week, and we played for over 3 hours (Singer curtained off, band spread out). Frankly, I was a little tired, but the bass (and my shoulder) felt fine that night and the next day, too.
I did upgrade the pickups to EMG Geezers, primarily because of the noisy and relatively anemic stock J. The Geezer J really growls and is noiseless. The P was fine before, and I didn't notice as much of a change with the P solo'd after the switch. The P in the Geezers is slightly hotter, but the tone is very similar to the stock P.
I also switched out the bridge for a Hipshot, mostly for cosmetics. The old bridge worked perfectly, easy to set-up/adjust. Capable of very low action, although I don't play with it set as low with my current (metal) band so I can dig in a little harder when needed. (I wouldn't claim that the Aerodyne is the best bass for metal, but it is capable in that genre.)
In true Fender fashion, it is easy to upgrade, setup, and maintain. I've done all work on it myself. Our singer, who also plays bass, LOVES the setup on my 'Dyne. The only way I can get it back from him is by starting to sing...
The 'Dyne does a great P-sound, but has the additional versatility of that J pickup. It was capable of a good range of tones before the upgrade, but I rarely solo'd the J before I upgraded. (I have a J for that.) But since I upgraded the pickups, I find myself favoring and even solo-ing the bridge for some stuff.
Complaints about the Aerodyne tend to be related to the more acute edge where the R forearm contacts the binding (for R-handed players), which some players find uncomfortable. I've never had an issue, but it is not rolled/rounded like most other basses. I think it's an issue related to how high you wear your bass. If you have a chance, you'd be wise to play one before you buy to see if that is an issue for you.
The other thing people talk about is the basswood body, which is a softer wood. I'm pretty sure the P-lyte is also basswood, so between these 2 basses, that would be a wash. I take good care of my instruments, but I don't baby them either. Mine is about 6 years old and still looks great. I've taken it to a lot of practices but it hasn't been gigged yet because I am just getting back into playing out again after a few decades off. But when I go, it will be there.