You should take the computer with 64 MB of dedicated video RAM. Shared memory is a nice term used by computer manufacturers to say that the video card steals however much memory (in your case, 512 MB) from the regular system. Although if you are looking at 6 GB of RAM it probably won't matter too much anyway.
I am looking to buy a new computer for use doing mostly standard things: word, internet, excel, photo management. I do also have Adobe Premiere Elements and I would like to start doing some editing of my home videos with that program. Though that won't be my main use of the computer, I want something that can handle Premiere and won't lag when doing any editing or playback.
I'm considering two different models (Gateway SX2802-07 and HP Pavilion p6204y), both with similar specs (2.6MHz processor, 6GB ram, 800MHz front side bus, 7200rpm SATA hard drive) but the main difference I can see is the video memory. For using Premiere, would 64MB of dedicated video memory be better, or 512MB shared?
Also, both of the computers I'm looking at have a front side bus of 800MHz, will that cause problems with video editing and playback?
Thanks for any advice, computer stuff can be very perplexing sometimes.