The VE is the crippled version with only one rendering pipeline. It is mostly meant for OEM's as a business card due to excellent 2D and built in dual monitor support. For 3D gaming it is at about a TNT2 level, so not the best bet if that's what your in for.
The LE is an OEM only version that got released in China and then found its way to North America. Basically, it is a standard Radeon 32Mb DDR that for whatever reason didn't pass ATI spec on the HyperZ (memory bandwidth optimization) function. It is also clocked slightly lower in both memory and core. Almost everyone who gets an LE is able to enable the HyperZ, and clock to at least standard speed. If you are comfortable with a few tweaks then it is definitely the better bet.
If you are looking for TV out specifically, make sure that if you do get the LE, it explicitly states that it has the TV out feature. Although I have seen TV out LE cards they are rare.
In sum, if you are a 3d gamer, definitely the LE. If you don't care, don't want to fuss around with it, and/or may want dual monitor support, then the VE is not a bad card.