I like both. Delta are very accurate and timely with both. I agree about coupons/bonus offers with the mailed ones but the instant accessibility on the web is nice.
ancient, inaccurate statments (Hilton anyone?) are more annoying than useful.

In the case of discrepancies or problems, I think that the paper ones carry a lot more weight and are therefore still useful. They can also be conveniently filed as a 'historical record'. As a tiny point, I love to get letters (especially ones that don't cost me money), so a few statements a month add to my pleasure and sense of wellbeing.

I am sure the main trend is toward online info and I can handle that and therefore live with it comfortably when it happens. It may be a problem for those who do not yet know the joys of the internet - do you think airlines will go online only with these things and when?