There is no Canon low cost option for the 135.
What...no love for the 135mm f/2.8 Soft Focus?!?
I have the 135 f2L and 85f/1.8. The 135 lets me get in closer to the subject and I prefer the shallower depth of field.
How close do you want to get? The MFD of the 135L is only 2" (5 cm) closer than 85L II. You're right about the shallower DoF - at their respective MFDs, the DoF of the 85L @ f/1.2 is 0.32" while the DoF of the 135L @ f/2 is 0.18". However, with reference to use on a FF camera, the 85L II at its MFD will frame a reasonably tight head shot - about 10" x 15", whereas the 135L at its MFD will frame 6.25" x 9.5", which starts cutting off the ears and hair, so you'll need to back up a little. If you back up enough to get the same framing, the 85L will give thinner DoF, obviously (since distance and focal length cancel with the same framing, so DoF is determined by aperture alone).
'Classically' (meaning from the days of film, when all SLRs were FF), 85mm was for torso shots and 135mm was for head shots.
Personally, I have both of the lenses the OP is interested in, and I also have both APS-C and FF. I started with the 85/1.8 on a 7D, really liked the framing for portraits - so much that I moved up to the 85L II. After getting a 5DII, I got a 135L to replicate the framing of 85mm on APS-C.
Given that you're starting on APS-C, I agree with the above comment that 135mm might be too long for portraits, especially indoors. On FF, you can do tight portraits indoors with the 135L, but the 85L allows more flexibility for framing. The other advantage of the 85L is that with the f/1.2, for the same framing the 85L will allow you to get a shallower DoF - sometimes that really helps blur out a cluttered background. Outdoors where you usually have more room, either lens will work wonderfully (but for both, you might want to invest in a 3-stop ND filter - on bright days, even 1/8000 s is not enough to let you shoot wide open).
OTOH, the 85L is basically a lens for one thing - portraits. The AF on the 85L is quite slow, and can have trouble keeping up with moving subjects. The 135L focuses very fast, and works well for portraits and also for action shots (it's a great stage lens).
So...IMO, if you want to pick one of the two lenses, you need to carefully consider how certain you are that you'll go FF soon. For APS-C, the 85L would likely be the better choice, IMO, whereas for FF the 135L would likely be better. FWIW, the 85L on APS-C is essentially equivalent to the 135L on FF (FF-equivalent of 85mm f/1.2 is 136mm f/1.9); I've tested them head to head - 85L on 7D vs. 135L on 5DII, and overall the IQ of the 135L on FF wins.
A reasonable compromise as suggested above would be to start with the 85mm f/1.8.
Some samples, the first with the 85L on APS-C, the rest on FF:
EOS 7D, EF 85mm f/1.2L
II USM, 1/2000 s, f/1.6, ISO 100
EOS 5D Mark II, EF 85mm f/1.2L
II USM @ 1/60 s, f/1.8, ISO 400
EOS 5D Mark II, EF 135mm f/2L
USM, 1/1600 s, f/2.2, ISO 100