I believe that 6s is the more competitive gamemode in TF2, from my experiences at least. Highlander teams tend to be more relaxed, and used as more of an entry way into competitive TF2, where as 6s is where the big boys play. I'm not sure what leagues are available but the one that I do know if is ESEA, and the only gamemode there is 6s.
That and UGC are the two currently going that I have participated in. UGC is Summer, started June 21 this year (might be the same every year). There is also IGL, and TWL that I have played in that seem to no longer be available. ESL and CEVO were also kind of popular that no longer have TF2. RTF2L was a Russian thing that I heard a lot about, but it apparently mysteriously disappeared. For European if you are from there or have good enough internet where ping isn't much of an issue, there is: ETF2L (Euro version of RTF2L), ESA, and I think the other is called Wiredplay. These are still all active.
There are plenty of leagues, and more that are country specific that I wont get into. TF2 should get slightly more popular soon before dying back down. TF2 probably doesn't have too many years left. They released so much new content so quickly, and the steam workshop is starting to get stale. But anyways, competitive play is still seen. And about 3/4 of them also have a Highlander division. The thing is that 6v6 is more different from normal gameplay, and there are a lot of cool things you can do with the common classes used for it. Let me tell you though, you can get pretty crazy as a sniper. Some videos I have seen from snipers in Competitive Highlander (Like some of the higher end UGC plat plays), and even some of the things I have pulled off myself (like head shotting a soldier in the middle of a rocket jump right after you land from jumping off a building), pretty intense. The thing is, that most Highlanders are Payload, which kind of kills it a bit, and the added Engineer and Spy makes it seem more like a fun game, since these roles aren't exactly competitive material (though I have also seen some amazing spy plays. Actually,a spy is a lot like a sniper, just up close and from behind, or using trickshots. Leave the engy to the demo).
Sorry for ranting, I just still have some leftover passion for competitive TF2 after how much I put into it.
