Having wheeled something with full independent suspension, front and rear solid axles, and something with independent front/solid rear, here are my observations:
1) Independent suspension means a MUCH more comfortable off road ride, especially if you're able to disconnect the sway bars. you can run trails a bit faster, and they are less jarring to your spine. BUT you find yourself on 3, or even 2 wheels quite often, meaning a locker or other traction device is almost required, since you'll often have 1 tire on at least one axle able to spin freely, thus getting all the torque, forward progression especially up hill was often an issue I struggled with.
2) front and rear solid axles. I'll admit my XJ had the Cadillac of suspensions, with dual rate springs in the front, OME shocks, and OME leafs in the rear, and it rode way better on and off road that most solid axle jeeps I had ever been in. That being said, Trails were MUCH rougher, and had to be taken slower. BUT due to articulation of the axles, I almost never had even a single tire off the ground, and so with no additional traction devices, (open diffs), places I struggled with my patriot, I had no issues in the XJ. The solid axles tend to be more robust, and can handle more than independent suspension setups on stock to lightly modified vehicles (the axles themselves are thicker/stronger, and have fewer fail points, like CV joints.)
3) independent front, and solid rear: the best and worst of both worlds. Maybe because I went from SUVs to a truck, but the ride is not as good as the patriot, and the articulation is worse than the jeep. If I had the $$, I would Solid axle swap the front end on my truck, no questions. It would have been done yesterday.
It comes down to really what you need/want. If I was doing mostly overland, light duty trails, independent suspension no questions, as long as it had a traction device (locker). if you do more difficult/technical trails, there is no contest that a solid axle setup is stronger, more reliable, and gives better traction in all situations.
as far as death wobble. 99.999% of the time, that is due to a loose track bar, and that is easily resolved by making sure the track bar is not getting loose. Whether the bolt has backed out, the hole it goes through is wallowed out, or the bushings on the track bar have started to fail, resolving the issue fixes the death wobble. and proper maintenance prevents it. (and it's super easy to check, just look at your front axle and have somebody turn the steering wheel left and right, if there is any play at all, it's super noticeable right away.)