Love the Oasis. Mary and I tried the Outfitter before the Oasis because she was told that it was more stable, but she said she felt more stable in the Oasis. I'm sure that had more to do with the fact that she was getting more comfortable being out in the water. (We tried them back-to-back down at Sellwood Park.) I didn't notice a difference stability-wise, but I sure noticed a difference in speed and maneuverability. The Oasis is much more fun.
We haven't used it out on the salt, but we have used it in heavy current on the Columbia several times, with no problem. We upset once, in knee deep water, when Mary sat up on the rail to check the rudder at the same time I was shifting in my seat just after getting in. Two people moving at the same time can cause problems, if they move to the same side quickly.
My guess is that your son is not heavy enough to affect stability as much as either my wife or me. I would think you would do fine with the Oasis. The Oasis is pretty much a twin Revo, and the Outfitter a twin Outback. The differences should correlate.
You might have noticed that I had a crossbar of 1-1/4" PVC mounted across the center. I am going to make some stabilizer floats from crab floats and PVC pipe that will attach to a 1" PVC crossbar that will slide inside the permanently mounted 1-1/4" PVC. I plan for the floats to ride just above the water, and come into play only when the Oasis is leaning. When I fish with my son James, I think the stabilizer floats may come in handy. Fishing with two people may lead to the aforementioned quick weight shifts.
Understand about having a fish on - I wasn't offended at all. I introduce myself as Sherman - NWKAers put the Sherminator together pretty quickly
Hope to see you again soon.