When it comes to the Isuzu Trooper, you've got two main choices for engine (at least for the 2nd generation which is the focus of this site).
You can go for the 'Devil's Juice' diesel, or the petrol option.
Depending on the age of the car, exactly where you are buying and so on there are a few different engine variants available ... but compared to buying a lot of higher-end SUVs, with the Bighorn you're not exactly spoiled for choice.
V6 petrol or diesel, that's all you can pick from.
This image from Garage Dreams' Trooper buyer's guide does a good job at outlining what options were available:
For American readers, you unfortunately only ever had (to my knowledge) the petrol engine option.
In this case, you're better to go for the DOHC V6 if possible, as the extra power is helpful and noticeable. The 3.2 V6 is generally found by most owners to be a smoother engine, but if you don't care so much about refinement and just want "poweerrrrr" then go for the 3.5.
If you live in Australia, New Zealand or other markets where you could get the Trooper (or any of its badge engineered variants) with the diesel engine, then this is the better option.
The diesel definitely has more reliability problems, particularly the later 3.0 diesel. The earlier 3.1 diesel is less powerful and about as sophisticated to drive as a sack of potatoes, but most of the reliability/maintenance problems are well-documented and fixable.
Although the diesel is an antiquated piece of kit, it suits the workhorse nature of the Trooper (at least for what I used mine for).
The diesel is better for towing, more economical at cruise, and you will notice the additional low-down grunt for things like off-roading or climbing up a skifield.
Whichever Trooper you buy, don't expect modern sophistication. These are old cars now. But they still have utility and work well for many purposes ... make sure you buy one with the right engine for your needs.