Day of Defeat: Source was, just like Counter-Strike: Source, an update to Valve's new Source engine. I'm not aware at all of how the original Day of Defeat fared, as I never played it, therefore I can't make a proper comparison between the two.
What I can talk about though, is obviously Day of Defeat: Source, having played it quite a bit and having fun with it. The game is set in WW2, and while a lot of games are set in WW2, nowadays with the massive trend of current and near future FPSes lately, it is remarkably a refreshing change.
Source obviously made the maps and models look much better than the original game. They still hold up quite well nowadays, much like Source itself in any case, so for most people there won't be much of a problem when it comes to graphical fidelity.
While I don't know how the gameplay in the original DoD was like, if it was anything like CS 1.6 to CS: Source, it may have ruffled a few feathers on the original DoD community upon DoD: Source's release. Or maybe it didn't, because of the gameplay.
The gameplay is most definitely this game's strong point by a long shot. There are several classes to pick from, varied enough to justify their presence in the game, and fully suit the setting, just like the various weapons you have. The shooting feels good, just like most of the FPSes in Source.
Unfortunately, it suffers from not having a whole lot of variety to it, both in game modes and in maps. And by now, there are naturally also other FPSes set in WW2 that feel and play a lot better than DoD: Source. There's still a community present, so you should have no difficulties jumping into a multiplayer game however.
I would get this game. It's cheap and can be an enjoyable and refreshing game experience once in a while. Plus it's a Valve game, and those come with a lot of obvious perks. (Garry's Mod models being an example) Just don't expect too much out of it.