It shouldn't matter which console you use. They're both going to be using the same source disc, and probably even the same chips to do the upscaling. Even if they both used their own proprietary software method, I would expect the difference to be minimal if all you're doing is a direct conversion. However, the PS3 has a bit more power for doing post-processing effects to try and enhance the picture more. I have absolutely no idea if this is included in the PS3 firmware or not, so it may be a purely academic discussion.
In the end though, you can get standalone DVD players that will upscale regular DVDs for less than $100US. I got a refurb model from Onkyo tossed in for free with a home theater system I bought from them not too long ago. Upscaling DVD players are nothing special, and just about every DVD player out there does it now to try and maintain some relevance before all anyone wants are blu-ray players. The drives on your game consoles, however, are the only drives out there that will play games for that particular console. You can always put a DVD into any upscaling player, but you can't just pop a 360 or PS3 game into the same player and have it work.
Optical drives DO wear out, and often a lot faster than you might think. So, if you ask me, game consoles should be left as emergency backup players. Something happens to your main player, it breaks, and you can't get to the store for a couple of days to buy a new one. Stand alone DVD players will tend to always be commodity, dime a dozen, products. Game consoles will always be unique and far more expensive. I'd rather spend the finite life of my console's unique (and expensive) optical drive playing games, not watching movies.
I own an Xbox 360 and will soon buy a PS3. I know both consoles will up convert a normal DVD via Hdmi signal. I was wondering if anyone knows what console is better at up converting normal DVDs?