From the makers stand point the difference is profound. D2 is non stainless 440C is stainless.
D2 is very difficult if not impossible to get as good polish on it as 440C but 440C can be brought to a mirror polish that looks very professional and finished, virtually with no lines visible at all. In fact because of this 440C is often used for making mirrors.
Both are considered premium grades of steel. D2 is perhaps harder to grind but has better edge holding and higher wear resistance. I like both steels. Some of my favorite knives are 440C and D2.
Even though D2 is technically a 'non stainless' it is the most stain resistant of the non stainless steels so it acts like stainless in many ways for many people and seems to hold up well. However, in some tests where D2 was used along side a stainless steel, I believe it was VG10 in this test the D2 outperformed the stainless until it came to cutting acidic fruits, and veges when the corrosive nature of the steel started to show. The D2 blade dulled significantly in the test after just a few slices in the acidic fruits and tomatos and for the first time in the test the stainless began to outperform it by a large margin.
So to me this says if you are planning lots of food prep chores with the D2 or perhaps lots of 'wet use chores' either stream side or under the faucet you are probably better off with the 440C blade. 440C is highly resistant to corrosion, pitting and/or rust.
If you don't mind more of a brushed look over a highly polished mirror finish D2 will be fine also. Otherwise 440C is a great choice.