[JRTJH]

Basically both types of bars do the same thing, lever weight to the tow vehicle front suspension. The trunnion bar system was developed by Reese as a part of one of their sway control hitches. On some (not all) hitch models, heavier duty bars are available only in trunnion style while on other brands, only round bars are available. On some brands, the choice is available in either style while in other brands, one or the other may not even be available. One of the major advantages of the trunnion system is added clearance below the bar attachment point. That clearance may become a "critical factor" on some applications where ground clearance is a significant factor. You can see the difference in "ground clearance" in this photo.

Essentially, the question: Which is better, round bar hitches or trunnion hitches? is almost like asking which is better, Ford, RAM or GM?

The answer is more "personal choice" based on type of hitch and brand of hitch. On some, there is no choice, on others, you can choose which type of bar you want. If all considerations were equal, it wouldn't much matter which type bar you choose. Basically, it comes down to availability and personal choice.