The 18XX has a reputation for being the heavy gamer's heavy game, to the point where there is a small but passionate number of folks who literally play nothing else. I enjoy them myself, at least to a point: I'm fairly rubbish at them, and because even the shorter ones take a while to play (with not-insignificant downtime) I haven't played any of them often enough to acquire any kind of competency. There's a learning curve for the series as a whole and for each of the better games in particular, and I'm still at the bottom of that incline, struggling to find my first foothold.
Here's the thing, though. That learning curve? It's not about learning how to play the game, just learning how to play the game well. The actual core rules of the 18XX are fairly straightforward and uncomplicated. While it's true that some of the games in the series are quite a bit more baroque, with all sorts of fascinating and indulgent curlicues and gimmicks, I would argue that the vast majority of the games aren't really that much more complicated than a medium-weight euro or an introductory hex-and-counter game. Setting aside things like permissive or restrictive track laying, or full-cap versus incremental - all of which is a little like the various kinds of ZOC (locking or elastic) in wargames, little bits of unique flavor and personality - it's not really hard to teach someone how to lay track, how to run a route, and how to buy and sell shares.
Compare this to other "heavy" games - including, yes, some of the heavier wargames - where a lot of the learning process is taken up with figuring out, and remembering, the rules. There are games Mary and I bought back during our euro days that we've played once or twice that haven't seen the table since, and that has less to do with my burgeoning apathy toward that style of game, and more to do with the fact that I'm going to have to relearn the game, and that if we actually got it on the table, Mary and I would have to struggle through it - every time we play the darn thing, it's a learning game all over again. There are too many moving parts, too many bells and whistles, and there is a sneaking suspicion that that is all there is: that the "depth" of the game is simply about wrestling with layers and layers of complicated whirligigs.
And I don't know if that's really depth. In a deep game, I make decisions. I might not always make the best decisions, and I might not always be able to comprehend the ramifications of my choices. What constitutes a good move or a bad one might be highly contextual, apparent only in retrospect, determined not by the moves that came before it but the moves that come after. I might not fully understand the decision I'm making, but at the same time I can see it, it's all there, all in front of me, unobstructed. If I'm holding my head in my hands, it's because my brain is slightly on fire.
Whereas with a complicated game, I'm putting my hands in my head (oh no!) because I'm confused. I don't think confusion is the same as "brain-burny", and I don't think complicated is the same as deep. In fact, I tend to associate depth with simplicity. That's not to say that all simple games are deep - they're not - but it is to say that many deep games are deeply simple.