This choice really comes down to what you mean by 'overlanding' and where. I have done a lot of overlanding as it might be described in the western US. All the trails in Ouray, a lot of trails in Moab including White Rim many times which would be considered the overland trail there, Mojave Road, big circuits in Death Valley, etc. 2-door Jeep JK with RTT. Those kind of trails are pretty much what you can expect for 'overlanding' in the US. Maximum maybe 3 days off-pavement, if you're going pretty slow about it. Either Taco or Jeep can do these type of trails fine. The jeep will have an easier time jumping into the more difficult trails which I would consider 'wheelin' or 'rock crawling'. Not that a toyota can't rock crawl, and everything can be modified so it becomes more of a game of how much you want to modify etc. The Taco will be better on pavement, no question. You will spend a lot of time on pavement getting between these places. I don't really mind driving the jeep on the road, but it can be kind of crappy in the real high colorado passes going up mountain expressways. It's a manual so that can make it more annoying constantly downshifting going up grades. But this is all part of the experience IMO. Taco will have a lot more space, especially than the 2-door jeep. However, the size of the jeep keeps us from bringing everything and the kitchen sink so to speak. We only have a little bit of room so we have to make choices and it's gonna be pared down.
If you are talking about somewhere outside the US there are a whole other group of concerns so I can't really comment on that.
A lot of these photos of huge Earthroamers and things like that make me laugh. You would for the most part be limited to the most mild of trails due to vehicle size. Most of the good trails in CO, UT, AZ, CA are narrow. I have plenty of pinstripes on my jeep which isn't real wide, I've had times when the height of the RTT on the top of the jeep is a problem, or switchbacks which take 2 k-turns to get my 2-door around. You would just not be able to get an Earthroamer, Sportsmobile, Bed Camper etc. down those trails. A full-size truck is too large for many of them.
One more thought on this subject, side by side UTVs have come a long way. They are extremely popular these days in Moab and Colorado at least. I was watching a whole bunch of stock Can-Ams and Polaris Generals on Hell's Revenge and they absolutely make it look like easy-mode bare-ass stock from the factory. If you are just interested in hitting trails and having fun then consider a nice full-size pickup (which you could camp in with either a camper top or a bed camper), and tow a decent side by side. I love my jeep but I have had to put a ton of work into making it tackle the trails that it does and I still have to be concerned about how it's gonna do on the highway. Compromises abound. If my jeep were totaled for some reason at this point I'd go with either a Tow Rig/SXS or Tow Rig/Tube Chassis Rock Buggy.