The 100-400L is a nice and convenient lens. It's a "push/pull" type zoom (one ring serves both manual focus and zoom)... some people like those, others don't. Personally I'm not a fan of push/pull, I just have had trouble getting sharp shots with them in the past (haven't used the 100-400 any more than briefly borrowing one, though... IS should help). Push/pulls are fast to zoom. A lot of folks think it's a near ideal lens for fast moving subjects, such as airshow photography. It's a reasonably compact lens considering the focal lengths it covers, has fairly quick focus and helpful image stabilization. It's around $1600-1700 U.S. If you get the 100-400L, resist any temptation to put a "protection" filter on it. A lot of users have found this lens very reluctant to work well with filters.
You might want to consider some alternatives:
I have and prefer using a 300/4 IS, with and without a 1.4X teleconverter. That meets my needs well, for a handholdable longer telephoto. The lenses themselves are close to the same size and weight, the 300/4 and 100-400. I use the 1.4X Mark II, which can be bought for around $250 used. The 300mm costs $1550... so the combo works out to cost about the same.
Another possibility is the Sigma 120-400 OS HSM. It's a more traditional two ring zoom, not a push/pull. It's also black, instead of "Canon white". Some folks really like both these features. It's just slightly larger in size and weight than the 100-400, both use the same 77mm filters, too. It has HSM focus, which is similar to Canon USM. It has OS, which some feel is even better stabilization than the Canon IS version used on the 100-400L. The Sigma seems pretty close in IQ, maybe a little lower contrast and saturation. It costs a lot less, around $1000 U.S. or less.
There is also the Sigma 150-500mm OS HSM. It's bigger and heavier (86mm filters) than either the 100-400L or Siggy 120-400mm. It's also a little slower... f6.3 at 500mm. But it's 100mm longer and a nice price, about $1100 U.S.
Sigma also offers the 50-500mm OS HSM. Nicknamed the "Bigma", it's a fairly big, heavy lens (95mm filter). But some folks really like it, especially at it's longer focal lengths. It's closer to the 100-400L in price... about $1650 normally (currently on sale for just over $1500, there's probably a new version coming soon... Sigma is updating all their lenses with some new features such as allowing users to upgrade the firmware or tweak the focus of the lens themselves).
Canon also offers the 400/5.6L. As a prime lens, it's not going to be as convenient as one of the zooms, but might be the sharpest pencil in this drawer. It also is Canon's longest lens without IS, which helps keep the cost down (about $1500 U.S.), but stabilization sure would be nice on such a long telephoto. There's a pretty big gap between your 135mm and a 400mm! (To keep things reasonably compact and manageable, with about a 22 lb. backpack, I've travelled with a wide angle, either 24-70 & 135/2 and 300mm, or a 28-135 and 300mm, using a 1.4X TC on the 135mm and/or 300mm as needed for 189mm and 420mm equivalents. But I wouldn't want that big "gap" between 135mm and 400mm... I too often need a lens around 200mm and 300mm focal lengths.)
All the above come with some limitations. With the exception of the 300/4, there are some limitations on using 1.4X teleconverters with the other lenses due to their f5.6 and f6.3 apertures. The biggest issue is that auto focus will not work or, at best, will struggle to work. For all practical purposes, they aren't usable with 2X teleconverters. They all mostly going to require good light... And/or a tripod (especially the 400/5.6 might benefit from some support, due to it's lack of stabilization). Due to size/weight of some of these, at least a monopod might be nice during long shoots, to give your arm a rest! (Though I sometimes use the 300/4 on one 7D all day long handheld. The 100-400L and Siggy 120-400 are similar weight.)
The most flexible option would be the considerably more expensive Sigma 120-300/2.8 OS HSM. It's at least double the price of most of the other options mentione (regularly $3200, currently on sale for $3000 U.S.). It's also a lot bigger and heavier than most of them, using a 105mm filter. At 6-1/2 lbs about twice as heavy as some of the other lenses. However, it can be used with both 1.4X and 2X teleconverters and in low light.
Everything else goes way, way up in price: Canon 300/2.8L IS, 400/4L DO IS (not very usable with teleconverters), 400/2.8L IS, 500/4L IS, 600/4L IS and 800/5.6L IS. The not-yet-released Canon 200-400/4L 1.4X has a built in teleconverter, but is likely to have a five figure price tag. Most of these are also a lot bigger and heavier.