The biggest issue most people have with the BFG is you no longer have to switch from flashlight to your weapon. This makes for a much faster, more traditional DOOM experience. the benefits are that the BFG edition comes with all the extras also. New and added bonus, 4k with Xbox One X BC, if you have a One X and your old 360 disc.
Personally I still play the original Xbox DOOM 3. The need to switch between flashlight and weapon slows down th egameplay and gives you that proto-Dead Space feel. It's a less traditional DOOM experience, but with 2016 out now, there's really no need to hold a grudge. It can be enjoyed on its own merits. The PC original DOOM 3 is likely the best route, as the original Xbox version had some stuff cut to make it work with less horsepower.