Lenses can't both front and back focus... one or the other... if it's out of adjustment it will be out of adjustment the same way, all the time. It will only vary depending upon how far you are from the subject and will be more or less obvious depending upon how large an aperture you are using.
Let's see. You have a $1600 camera, $200-300 zoom and a $100 prime... hmmm. Methinks something is backwards. Still, that shouldn't effect AF, except that some lenses are slower to focus (your 50/1.8 is likely slower than the 28-135, in this case).
But, frankly, I find I have more "missed focus" shots with 7D than I did with 50D. I probably get 85% to 90% accuracy with 7D, but consistently got around 95% or better with 50D.
28-135 is a decent performer. Probably sharper than a 50/1.8 in some of it's focal lengths. By any chance, you aren't sticking it on a tripod without turning off the IS, are you? That would make for "fuzzy pics" a lot of the time.
Another thing, with IS lenses you have to give the stabilization a moment to do it's thing, before taking the shot. If you shoot too fast with IS, you can get fuzzy shots that look out of focus (but are actually blurred entirely). It's not a long pause, IS takes about as a half second, about the same time it takes for AF to lock on (which is happening at the same time).
Aside from that, that lens' USM autofocus is decently quick and precise.
A couple general points....
Switch to using just the center AF point on the camera. That will be more precise, but you'll have to be more careful keeping the AF point on your subject. You can use other individual AF points for off-center compositions, if you have time to select them. Otherwise, you are leaving the point of focus selection up to the camera, and it's just guessing what you want.
Next, use AI Servo for moving subjects. It's okay with static subjects, too, but One Shot might be more accurate sometimes. I never use AI Focus... It's supposed to choose from the other two, when it "senses" that the subject is moving... but it generally just slows down AF.
Technique is important and comes with practice. I use the "thumb focusing" method with all my cameras, separating the AF function from the shutter release button and reassigning it to the * button or the AF On button only. That's more accurate with moving subjects and is a popular technique for sports photographers using Canon cameras. It also allows recomposing, after focusing, with static subjects. Takes a little practice, but is easy to learn.
You can more exactly test your particular lens/camera combo. Use a tripod, turn off IS, focus on a ruler set at an angle and focus with One Shot. Take a shot, refocus, take another shot, refocuse and take a third. Look at the shots and see if they are front or back focused. The 7D has Micro Adjust, so you can set that for your lens. There's more info about this in the camera manual or possibly on Canon's website. With a zoom, you'll have to test at the wide and long ends, at least, then average the adjustment you dial in. You can Micro Adjust up to 20 specific lenses on the camera.
There is a greater need to Micro Adjust lenses with higher resolution cameras such as the 7D. You will tend to look at the images much larger on your computer monitor, so are more likely to see even very minor AF errors. This is especially true is you are used to viewing smaller, lower resolution files. Try not using 100%, but 50% or less when viewing the images.
If unable to get the focus set more precisely with Micro Adjust, you might need to send the camera and lens in to Canon service for adjustment. It's more likely the camera than the lens out of adjustment, so a new lens might not solve the problem.