Just came from a 2004 STI. Note I had it rather heavily modified. GT3076R turbo, 44mm wastegate, front mount, <insert laundry list of crap here>, but I started stock at least.
It seems both mod well. It is very easy to add 40-60hp to an STI, and they're still quite reliable with a moderate turbo upgrade. Downpipe + tune = 60hp on an STI. Parts are way cheaper on an STI. I'm still balking at $1000-1600 just for a catback. The nicest turbobacks for an STI are barely $1k. Transmission is practically indestructible. Ring lands will break IF you have detonation. Too many people throw blow off valves (bad on a MAF based fueling system), manual boost controllers (stupid!), and intakes that screw up the MAF transfer function, etc. on their cars and don't have them properly tuned. They run lean into boost briefly on the factory tunes at of about 07+ and it is ok, but if you add a downpipe and don't have it tuned immediately it can be devastating as it will knock and eventually blow. The EJ257 engine is a good engine otherwise, but people do stupid things to them. Keep in mind as you read anecdotal evidence of people blowing EJ257s that there are a crap load more of them out there with more miles.
135 has less lag and a better boost threshold, but I question people quoting 4000rpm for an STI. It really shouldn't be that bad. In 3rd gear it should be around 3000-3200rpm. Lower RPM in higher gears. It will spool on the highway in 6th gear at 2400rpm. The STI turbo is a few feet from the heads, so the coupling is looser. STI is slower to react in lower RPM, and comes on a bit softer. 135 sometimes seems to just "snap" to boost and it almost feels like a hesitation issue with how it comes up. Different feel, but yeah the 135 has much better grunt down low.
STI has much more mature aftermarket. Big rotated turbo kits with external wastegates, bolt-on midsize turbos, fuel system upgrades, a number of tuning options. In particular, Open ECU allows you to tune your own car on the cheap if you're interested, and it works on the raw ROM/BIN right off the ECU if you are so inclined to disassemble it yourself. Cobb AP is another good option. Dozens of cheap downpipes, catbacks, several equal or unequal length headers, all sorts of wheels, carbon fiber parts, everything you'd ever want suspension wise...
STI is very front heavy plus AWD so understeer is more pronounced. Brakes are pretty close. STI has a better shifter and clutch feel. Both have a very precise steering feel, though I'd give the 135 a very slight edge. STI is louder and more obnoxious in general. 135i is far more understated and "classy." Of course many people end up throwing loud exhausts on their 135i anyway.
STI is cheaper by a few grand (not to mention aftermarket parts prices are WAY cheaper), though you could argue about options. I think it is far to say it is about $3k cheaper similarly optioned, and the 135i has a much higher ceiling on options. STI stops at about $39k for Limited with nav unless you start adding dealer crap like Teflon paint coating, blessing by local pagans, fuel line magnets, etc.
However, in some respects they're not the greatest comparison...
For those in nothern states that need to get to work 365 days a year even in snowstorms, the STI (with a set of all season or winter tires) is a ton of fun. With three limited slip differentials (center being electronic/close loop) and either 40/60 or 35/65 torque split it is amazing a car like that can also drive through 8+inches of snow like it wasn't there, or pull an effortless 4 wheel drift around a roundabout on sheer ice.
STI is a four door and four reasonable sized adults can fit in it, and get in and out of the back seats comfortably. That's a rather huge difference. The 135i is almost more comparable to a 370z in that respect as it is almost more of a 2 seater. STI passes the, "Would you load your 60 year old parents into the back of your car?" test, and the 135 does not.
The four door or cold weather elements may be the real deciding factor for you. The STI can be just about anyone's one and only car, 135 is questionable filling that role for some people. For me, I've got a backup car for the few horrible winter days and no family, so I'm switching over.