I prefer "broad" in the way I would define "broad," which is neither "narrow" nor "desultory." I suspect a lot of things I would consider "desultory" are what others would classify as "broad."
For me, a "narrow" class has a small number (say, 4 or less) rigidly fixed paths. You don't get meaningful choices, nor can you "drift" (if I'm using that term correctly) into other ways of doing things. E.g., if every Cleric is a heal it, but some are endurance healers (low rate but high volume), some are mitigation specialists, some have limited but huge heals (high rate but low volume), etc., and cannot become anything else, then I would call that too narrow.
Conversely, a "desultory" class is one that gives you zero structure or guidance. Instead of rigidly fixing you on one and only one path, it seems to go out of its way to eliminate any guideline you might follow. The 3.X Fighter is a great example here. The idea was supposed to be huge freedom and variability due to the massive pile of extra feats, but because good feats were almost always locked behind piles of bad (or at least boring) feats, the implementation was extremely poor. It's well known in 3.5e charop circles that building an effective Fighter is an extreme challenge, something only for real charop experts, because it is just SO easy to get it wrong and end up with useless crap.
A broad class avoids these pitfalls. It offers clearly-defined starting benefits and functional guidance on what to do, while offering real choice and internal diversity/variation without ironclad limits.
As far as I'm concerned, most 4e classes were "broad" by this definition. They gave you a reliable starting point and a good idea of how to move forward...but left it up to you whether to do that or to pursue something else instead. Between Themes, Paragon Paths, and the multiclass or hybrid rules, you could do just about whatever you wanted, and have a good idea of whether it would be worthwhile or not. Certain options, particularly later on e.g. Vampire, fell short of this goal.
For comparison, I find both the 5e Fighter and 5e Wizard to be desultory. They do nothing to set you on a productive path, they barely if at all support their theme, and they contain several "trap" options or flawed implementations. And with how shallow the mechanical elements of 5e are, it's hard to do much of anything to redirect things or alter your course.