There is not a shred, not one shred, of scientific evidence that shows that HDMI cable quality can improve or degrade picture or sound quality. With HDMI, if you get the picture and sound, then you will be seeing it exactly as you would on a £500 cable. You either see the picture or you don't, if you see it you get it as it should be.
The data is digital, 00110101 is 00110101 and nothing else will do. Ah, you say, surely interference could change this to 00110100 couldn't it? Well, yes. But here's the catch, there is something called a checksum sent along with the data stream which lets the receiving device (the TV) check the integrity of the data it has receivied. If it is changed, by even a single bit, then it is detected and gets rejected. This happens in all things digital.
Put it this way. If you upgraded the cable betweeen your ADSL router and the telephone, would web pages look any clearer? No, because the data is digital. If you download a picture as part of an email attachment on a slow or unreliable Internet connection (a mobile phone for example), does it look any different to how it would if you had downloaded it on a corporate connection that uses dark fibre optic? Of course not. You either get the attachment or you don't.
As for 1.3, this (as you all undoutedly know) brings a number of new features like deep colour that need a higher data rate. Some cables claim to be capable, others don't. But once again, if you have a 1.3 capable source and TV, and you are getting a picture, you are (subject to settings) getting the 1.3. You either get it or you don't.
The only, absolute only thing that an expensive HDMI cable may (may) be able to do is show a picture over a long or difficult run that a cheap cable couldn't, or provide a higher standard (1080p instead of 1080i for example) but once again, it's the difference between seeing a picture (or hearing sound) and not, it CANNOT affect the picture.