I have played all of these in the past, but HON only briefly so I can't give too much input there. I found LoL to be the most fun, particularly with friends when just playing normals, and probably the easiest to get into (however, all the games here have the age old 'tough to master' approach to them). League has the problem that the match-making system is utterly dreadful and the community is probably the most toxic thing ever to crawl out of the internet cesspool. It also lacks a South African server. The ping is actually fairly alright most of the time, but you could never really hope to play at your best with the slightly lagged response time. I play League quite often and really enjoy it about 80% of the time when these issues do not arise. LoL is also a lot more forgiving. Your team can easily make a ridiculous comeback regardless of how well the other team is doing, depending on team composition and whether or not the losing team can actually outplay the opposition long enough to turn the tides (but often, it just takes one cock-up from the opposing team to turn it around). In DotA, the team with the advantage typically always wins (as in, wipes the floor with your poor under-farmed and under-leveled face).
DotA 2 is a much better experience in general. The game is far more stable than LoL's client (as in actual stability, performance, and useability), and it has a proper AFK detection and punishment system with the option to pause should someone disconnect from the game unexpectedly (which is common with South African internet, and the community here in SA is nice enough to wait for fair amounts of time). It is a lot more difficult to get good at, though. The learning curve is very steep, and it is quite important to know how each hero plays in order to counter them effectively. It will take a lot more time to get used to all of the mechanics, but fortunately plenty of new players are dropping in lately for relative newbies to get acquainted with the game. DotA 2 is just better designed in almost all aspects, but that doesn't necessarily mean LoL is a bad game. I probably play more LoL than DotA 2, which is where the opinion of DotA's design advantage stems from.
So, all-in-all, DotA 2 gets my vote for its general superiority. I still get my arse handed to me regularly by far better players, though.