D2:ED is a continuation of the series. The plots of DD and BD, as well as events in between all three games, are described and referred to throughout at least the start of the game (and likely most of it), though that is more for atmosphere, and knowledge of the previous games is not required to play the latest.
I'm only a quarter or so through the game, but so far I'm enjoying it at least as much as DD. The music is a little bit better (and I burned DD's music to a couple CDs), as is the humour. The quest system is better in D2:ED, with multiple choices in many quests and different outcomes that follow (nothing that makes large scale changes to the world, but it is nice to have options). The environment is very nice; there isn't as much world interaction as in DD (no rearranging furniture, etc), though the alchemy and charm systems are more involved, and some equipment can also be enchanted/unenchanted.
The combat system in D2:ED is more flexible, without needing to micro-manage. With the right skills/stats/equipment you should still be able to click-fest through opponents that are not too much higher than you in level, were you so inclined (though you can not spam healing potions), but you can often use the environment or a slightly more thought out strategy to your advantage. Currently I am dual wielding axes as my main attack method, but tend to explore with a bow readied; a bow is the easiest way to break barrels/crates for loot, and it can be handy to start off combat (especially against melee opponents). Rush Attack can be great for melee characters to be able to get to mages or archers quickly, but if you jump into the middle of a group of archers and mages, you are not necessarily going to be better off than if you had let them come to you. Combat is a bit too much level dependent, though; opponents too much higher than you can be very tough, while 3 or 4 levels below and they stop being much of a threat. At least so far for me there has always been somewhere else to go if a certain area is too tough (same as with DD).
I was a bit disappointed you couldn't use a pot for a helmet or swipe a farmer's rake for a staff (not that I did than in DD, but it was cool that that was possible), but at least your character in D2:ED can jump over 2 foot high earth ledges, the bane of DD's Divine One.

I'd recommend you try out the
demo (1.8GB), and/or check out the trailers on the
official site or gameplay videos on Youtube. Saving is disabled in the demo, but if you die I think you can reload the last auto-save.