OK, the theory is that a full tang is stronger and often it will be, but not always, and a whole load of variables come into play which are about as interesting as watching paint dry to discuss
Those variables can include how well the shoulders of the hidden tang were rounded and finished prior to heat treating to avoid stress fractures during quench and before first temper, and to encourage good stress distribution under load, how well any holes were countersunk to avoid similar issues, the time between quench and first temper, whether or not the blade was cryo treated (which is about the best stress reliever there is for steel and the main reason why I soak most of my blades for 24 hours in liquid nitrogen), whether the window of oportunity to get the blade down below its critical range on quenching was actually hit square on (which can be the single biggest cause of introducing stresses into the steel) and whether...
You get the idea.
I'd ask in return, how strong is strong enough or, instead, maybe we should ask how do you consider your current knife to be below the bar ?
This comes largely down to use and, while I can admire anyone who goes minimalist (been there, done that), you can't get away from the simple fact that any knife you can easily carry and handle is normally a slicing tool by definition. Unless we are talking about much larger knives, they aren't for chopping.
Just because you can baton with a knife does not necessarily mean that you should. That's what saws, hatchets and machetes are for.
Over the last few years I've seen a few spectacular breakages and, if you refer to my post above regarding blade hardness in relation to heavy use, a knife intended for hard batoning should be several points softer than a slicing knife. If it isn't, sooner or later you're going to get a nasty shock.
A friend of mine recently had a very expensive and well known full tang knife break on him during his first outing when batoning with it, and I can think of three similar instances that I have witnessed in the last couple of years or so, and a bunch of others I have heard of, involving anything from factory to high end custom knives.
For my own part, I could (usually) get away with a small slip joint folder for most of my outdoors knife work since I confine its use mainly to food prep, trimming plants, green wood and cordage and whittling trap triggers/pot hangers etc.,
My main outdoors fixed blade knife reflects this usage, being thin, very hard and seriously sharp, and it is never at risk because it almost never does anything than slice, and it requires only a strop to keep it running this way for weeks on end.
If we were being purist and using flint or obsidian blades we'd never consider batoning to begin with. Small game, fish and birds don't require a knife at all to process, though it's faster and less messy if you have one
Choices seem simple to me - gear up (add a saw to your kit and enjoy the benefits thereof), or tone down what you are demanding of your current kit.
Stick a slip joint folder in your pocket next time you go out as your backup device. Most times when folks try this they end up using it more than their fixed blade. Small, thin and sharp always does the business.
This raises the question of likely use. In real world use a debris shelter is often quick and easy to make, and requires no tools. Constructing a shelter using only a knife and some string is a chore if you are cutting every component part. I guess I am more used to bending, breaking or simply using it as it is than using a knife to chew my way through a stand of timber.
If I was that concerned about a smaller hidden or half tang knife I'd be upping the game by choosing something significantly bigger, a little software, that can easily be used for heavier chopping but can still slice. Your average 4" bushcraft knife fails the brief in so many ways in this scenario, and replacing one 4" bushcraft knife with another 4" bushcraft knife with a different tang seems like a sideways move at best. Especially where funds are limited - I'd suggest holding onto your money and stick, rather than twist.
Good luck with whatever you decide upon.
I'll get my coat...