Yes, as Andre-Georg says, there is one significant mechanical difference, which depending on the year of DII, you may have, could possibly add, or may have no hope of getting. Of course, maybe the CDL isn't what A-G was referring to...
I have a 99 DI and an 04 DII. As you'll probably see here and on other popular Landy websites, each vehicle's history of mechanical shortcomings will be influenced by how well it was maintained by previous owners (if any). That said, I have ~109k miles and my only major problems have been leaky head gaskets and a leaking steering box, both of which seem to be common. I had the gaskets replaced about a month ago, and a couple of weeks ago the steering box was replaced after an oil cooler line rubbed a hole in one of the steel lines external to the steering box.
Anyway, I love my D1 and the relative simplicity of working on it. Granted I haven't suffered many Lucas gremlins yet. Mike is dead-on when he says that the DII is more comfortable on road. I wouldn't know off-road because my wife isn't too keen on getting 'her' Disco off the beaten track. It's hard enough for me to take it into loose terrain occasionally to exercise the diff lock. Someday she will tire of it and then I'll get to break it in properly...
I digress. I recently drove an LR3 off-road and now I'm hooked on HDC! The larger cargo area in the DII is nice, too. Bottomline, there are pluses and minuses to both, so a lot comes down to personal preference and budget.
I'm assuming you're in the US? Good luck and welcome to the Land Rover world!