Well, the first thing you'll notice is the small rear LCD and the fact that you just won't find it very useful for analyzing your images. A lot of us just use it for the histogram, highlight alerts, and just the most general glance at the image to make sure something didn't go really wrong!
But then, one of the other "first" things you should notice is that it has a nice big and bright viewfinder to show that full frame image! It doesn't quite offer 100% coverage, but it still is nice to use!
Image quality is still great, even after all these years
! True it's ISO limited -- if I really need ISO 3200 or higher, I'd grab another body (my old 1DM3 delivers there) but I really prefer not needing that high ISO for my day-to-day shooting. The 5D is great at its native ISO 1600, and if you really want/need 3200 it does have the "Expansion" ISOs of 50 and 3200.
But, despite all the good that can be said about the 5D Classic, it's still an older body/technology. If you've never shot with one or, say, a 20D or a 30D (they have the same body design), then you may find yourself really set back in using the 5D. In fact, I'd suggest I'd suggest trying one out for a while before making the leap.
Now, a lot of us 5D owners actually enjoy shooting with it, old "classical" features and all, but that doesn't mean that we would turn down, say, a 5D2. It just means that it's nice to have the old familar 5DC in your hands, and to get nice images out of it!
Now, one thing you'll hear about both the 5DC and the 5D2 is the "lousy AF". Well, true, it's outdated, sure -- it is an improved version of what you get with the 20D/30D, but still is not the best around any more. So, in low light it can struggle and the outer points can become useless, whereas the 1D bodies and now the 7D boast some amazing AF capabilities, and I gather the 50D and 60D bodies have a pretty nice AF.
But you know what? I've been shooting with the 5D for four years now, and still it is one of my go-to bodies, especially for, well, anything that I can take my time with and that doesn't require the high performance of my 1D3 -- birds, wildlife, sports, and some types of event photography.