The soil/ground conditions and the sheer weight of the tractor relative to flotation, is what will dictate performance, or you getting it stuck. That in simple terms is a given.
You have to learn the limitations of the tractor in the conditions you have, and it sounds as if what you were operating in, was plainly not suitable for a wheeled tractor, well at least the 3400, being substantially heavier.
If the ground is soft and or it pumps because of that, you may have one or 2 passes before it fails and you sink. The front narrow ag tires will slice open soft ground ahead of the rears and the rears will follow that path right in to sink instead of float. This makes it real easy to get stuck with that kind of arrangement, the wider flotation tires will perform better, but with limitations just the same as wet ground is wet ground, too much moisture, not even an LGP crawler with 36" track pads will operate on it. At that point you get into specialized equipment, matting or whatever it takes. Sometimes you need to be able to reach in, say with an excavator, from dry or stable ground to get the work done on a pond, these are ok for some earthwork, but digging ponds with a slip scoop or rear blade is a lot of repetitive work that will soon trash any kind of wet area.
I have ground like was mentioned below, hard under a foot or so of muck. Ballasted tires may help there, but I've never been able to really compare the 2, I have had one tire not loaded, gotten stuck, with that side up on hard ground along something like you described but parallel to it, not crossing it.
I suppose having a lot of experience has been helpful, personally I operated heavy equipment for 5 years full time and we worked some wet sites that were miserable, you kind of get the feel for it, making drainage and all that is involve, less experience, you just get stuck more often, but you do learn LOL !
Even then I still buried my 850 last year. One other thing that can be a problem, is if your steering is not tight or has enough play for the front wheels to make drag or resistance like mine did. I have been through this area for years, sometimes this corner is wet, most years its dry. Last year it was not hot enough for long enough to dry out, fronts sliced in, the play in the wheels made more drag, the back lost traction and churned in almost to the main housings, it sank eventually and was hung up. I have made 12" ruts in here once before and pushed my way backwards while in reverse with the bucket and a 6' rotary mower on, and did not get stuck, there was hard ground under the old top soil, this was crop land years ago.
I tried all the tricks, log to the wheel, forget it, no good. I waited as the conditions changed and it dried out. What eventually got it out was a chain hoist rigged to the base of a very small diameter, young black cherry tree, 4"-5" diameter. That and a friend to help.
This year, in defiance, I ran right through there with the 4630 fwd, the front tires alone made the difference, flotation is key, I did not use fwd, however if was running through there an worked it all up, sooner or later that tractor could have traction issues, sometimes its just not a winning proposition to run in wet ground with a tractor.
You can see the progression here, initial stuck, then after fooling with it. I've never been one to just spin the wheels, but all the attempts just made a mess, water ran in, it flooded. I learned that a chain hoist is a very valuable tool that can be used to move something like this slowly, that and the base of a small tree can be all that you need to get it out.