As a B&O shop manager, I've sold a lot of these, so I'll give you the best advice I can. At least I don't have to worry about sounding biased here on the BeoWorld forum!
Interesting question in terms of a non-B&O panel. Obviously the ideal compliment to the BeoSystem 3 would be a BeoVision 4 and if you walked into my shop I'd be hard pressed to let you get away with a major investment like the BeoSystem 3 with another manufacturer's panel!
That being said, the BeoSystem 3 obviously offers a major upgrade in form (I think you can fit almost 11 BeoSystem 3s inside a BeoSystem 1) and in connectivity. I'm not sure where you're located, but here in the US, many of our clients demand multiple HD sources and the BS 1 simply can't do this very well.
As for the picture, I've actually hooked BS3s up to several old panels and seen an absolutely remarkable difference. Blacks are deeper, but also offer more definition. Colors are richer, but still very realistic. Motion handling is, I think, the most impressive difference.
That being said, I've also hooked up to BeoSystem 3s to other panels (Sony LCD, Samsung LCD, Panasonic Plasma) and of course I haven't done a side by side comparison with those same panels hooked up to a BS 1, but I've found that there are only marginal improvements to the picture. Unfortunately these panels are only capable of so much.
I think that it's important to remember how symbiotic the relationship is between the BV 4 and the BS 3. While they are phenomenal products in their own right, they are designed to work together. All the active picture controls work exclusively on the BV4, so the BS3 is not fully utilized when paired with other panels.
My honest advice after selling B&O for almost 8 years is that customers who pair the processors with other panels never quite "get" the B&O advantage. I think that you'd be better off hooking up the BS 3 to an older BV 4 if you really have budget concerns. You will never regret a BeoVision 4 purchase, but I can tell that after years of pairing our processor with an LG panel that you have yet to experience all that a BeoSystem processor is capable of delivering.
Good Luck!
There is scarcely anything in this world that some man cannot make a little worse and sell a little more cheaply. The person who buys on price alone is this man's lawful prey. - John Ruskin