Better quality/branded PSU's tend to:
Use better components (more reliable, longer life).
Have better designs (more stable/able to cope with closer to the stated max power for longer, or even go over for short periods of time, run cooler extending the life of it's parts).
Have much much better protection for the connected PC - things like better filtering against minor changes in the incoming voltage, better protection against short circuits, better protection against over voltage and better protection against over current.
Basically, a cheap PSU will tend to be older designs, made with lower quality parts, and without some/all of the protections the better ones have (they'll meet minimum safety standards for the EU etc, but that's protection for the user, not the connected equipment).
Or to put it another way:
Cheap PSU encounters a problem that causes it to blow (much more easy to do with a cheap PSU due to design issues) - it'll be much more likely to take things like the motherboard, GFX card and drives with it.
Branded PSU fails - chances are good that the secondary protection on the output (PC) side will minimise/stop long term damage to the rest of the PC.
Not to mention Cheap PSU - might claim 550watt, but only manage that for fractions of a second, with the real longer term maximum being 300-400watt, whilst a better PSU might claim 550watt but long term be happy at 450-500watt or more with more headroom for things like start up surges.
As a fairly good example of the difference between a cheap PSU and a good one of a similar claimed wattage, I've had PC's here that have been running when the lights have flickered.
The PC with good PSU just kept running without a hiccup, the one with a cheap PSU suffered a reboot despite the fact the components it was powering requiring a lot less power than the one with the better PSU.