It does not seem to be a back/forward focus problem - just lack of capability to achieve sharp focus.
If I focus using the sensor in live view mode - the focus is almost always tack sharp - or at least much better, even wide open at 1.4 - and beyond 2 tack sharp.
1) Can someone explain this phenomenon?
Why do you think it isn't a back/front focus problem? I ask, because what you describe sounds like a classic case of a need to adjust your AF - the phase detect AF is off a bit, whereas the contrast detect AF (Live View) is spot on. Phase detect uses a separate AF sensor, which may be slightly misaligned relative to the image sensor (that misalignment can affect different lenses in different ways). Contrast detect uses the imaging sensor, so there's nothing to be aligned/adjusted.
Granted, the 50/1.4 has some halation wide open, and that results in a slight softening of the resulting images - but if they're sharper using live view, that really points to an AF issue.
AF issues (front/back focus) are most evident in shots with a shallow depth of field (like you get with the 50/1.4 at a wide aperture). A similar issue on a typical consumer zoom (f/3.5-5.6) would likely never be noticed. That's also why you aren't noticing an issue at f/2.8 and narrower - the deeper DoF masks focus errors.
Is this reproducible, e.g. does it happen with different subjects? That's important, because one thing many people don't realize is that the actual AF point on the AF sensor is larger than the little box in the viewfinder. That means that your chosen focus point may have features that cause your camera's AF system to lock onto something you didn't intend, even within one AF point. See the attached image below - a member of another forum was compaining that two successive shots with a 135mm f/2L had different focus, but when I superimposed the center AF point of the 7D (the camera used by that person), you can see that the AF system was merely locking onto different features of the key each time. You can also see how the actual AF point sensor is alrger than the representative box in the viewfinder.
The ideal way to test AF performance is with a commercial tool like a LensAlign or SpyderLensCal - those have a focus target that is parallel to the camera (and aligned properly), and a readout 'ruler' at an angle to the camera. Since buying one just for this seems unwise, try printing this starburst target
, then tape it to a box on a table, and line up a row of somethings (batteries work well) next to the box, extending toward and away from the camera. Focus on the target straight on, and see which battery is in focus (the one adjacent to the target, or forward/backward of that). Compare phase AF and Live View. A tripod would work best, assuming you have one.
2) Would a more advanced body (say a 60d ) have better autofocus results ? Is there a difference even using the CENTER focusing point between the 550d and the 60d ?
There might difference between the center AF point in your camera and a more advanced body. The 60D (and 40D/50D) as well as the 7D have a more complex center AF point. Yours has two lines, one sensitive to f/5.6 and the other sensitive to f/2.8 (the 'high-precision' part). The xxD and 7D bodies have a +-shaped f/5.6 sensor with an X-shaped f/2.8 sensor superimposed on that, so you're getting the f/2.8 presicion in two orientations instead of just one. But as stated above, I don't think that's the problem in your case.
If the problem is a misadjusted AF, a more advanced body would help. But not the 60D. The feature that allows a user to correct AF issues on their own is called autofocus microadjustment (AMFA), and the 60D doesn't have it. The current xD bodies have it (1-series, 5DII, 7D), as does the 50D (but Canon dropped AMFA from the 60D, for no apparent reason other than to differentiate the lines, as it's a no-cost feature). Personally, I'll never by a body without AFMA - all of my AF lenses have some amount of adjustment applied, but it's most important with the fast primes.
Hope that helps...