I've had my 03 LMB M5 for a week now, so I suppose I'm qualified to respond...
I was just at the local BMW dealership, so I had a good look at the more recent examples for comparison. My opinions:
Exterior styling: The E39 is still a very nice looking car. I think the more bulbous lines of the E60 may be practical in that they provide greater interior volume, and other designers seem to be copying the "shark eye" headlights, but I still think the E39 is a classic, balanced, elegant design that manages to contain a practical, 4-seat interior with some reasonable trunk space. Don't get me wrong, I love the styling of a Ferrari Dino, but I don't know where I'd put the hockey bag and sticks...
Interior: I think the E39, particularly the M5, has a *very* nice interior. Mine has extended leather, and it generates a warm, luxurious sense that the newer ones don't seem to have. IMHO, the newer ones have more of a sterile, modern minimalist feel, like a glass and stainless city condo. For reference, it also trumps the interior of my 07 Lexus, which has more exposed plastic than the Housewives of (pick your favorite city).
Driving: I think this is the main area where you may notice a difference between newer cars and a particular example of an older M5. If all is in proper running order, the M5 should match/exceed anything that doesn't cost 2-3X more, e.g. E60 550i, M5. However, many cars are driven pretty hard and not all are looked after. When I was looking, I found most were driven hard until enough things were broken that they were traded or offered up for sale. Those wouldn't match up with a newer car whose components hadn't yet worn to the point of being noticeable. If you find an example whose suspension/steering/motor are in good shape, I would be truly surprised if newer was any better unless you spend a lot more $.
Other: One appealing aspect of the E39 M5 is that much of the maintenance/repair is possible to DIY, especially with the advice and information shared on this board. Having owned an E39 540i6 for many years, I've accumulated tools, parts and confidence to look after the M5 that I'm not sure I'd have if I went with a newer, more high-tech model. For example, having to introduce a new battery to the car's computer is the sort of dealer-only service that drives me nuts. If you are willing, you can extend the relatively low cost to acquire a true supercar to a reasonable cost to keep it running like a supercar - not as possible with most other cars that can keep up with or outrun an M5.
My $0.02 only - for what it's worth,
ES