Both chain and gears have their own strong and weak points and either could be used correctly or incorrectly.
If you tension the chain too much - you get a ton of extra friction, but gears are not immune from that either, if you don’t secure all bearings or don’t align all the axles properly.
If you have too much slop in the chain, or sprockets are not perfectly aligned to be in one plane, then it could easily break from sudden shocks.
In general, I would use gears if you need to transfer power over the short distance and chain if you need to do it over the long distance. Each axle adds additional friction and having geartrain going all the way from one side to the other is not very practical.
In the ideal chassis you would have all four wheels directly powered by a motor with chain connecting front and back wheel. This way it is used only in case if front or back wheels lose traction and you need to transfer excess power to the other side.
The trick to use chain is, first, to align the sprockets perfectly in one plane, and then make sure there is neither extra slop nor extra tension, to minimize friction. You need to do a free spin test (when motors are not connected) by initially spinning the wheels by hand and having it run for, at least, 8-10 sec after that. Otherwise, something is adding extra friction and you need to fix that.
Another good habit is to inspect the chain for any loose, tight, damaged, or crooked links. Each could introduce their own potential issues and it is always pays off to spend 1 hour at the beginning of the season and not having to worry about chain snapping in the finals, or when you need it to work the most.