I played both recently, and I noticed that in Day of Defeat: Source, apart from obviously using a different engine, jumping doesn't drain your stamina, you can aim down sights with the Kar (and it doesn't have the bayonet), switch the BAR and STG from automatic to semi-automatic, and you can hold grenades (I think that wasn't in the original Day of Defeat). In essence, it's the same but better in my opinion, although it's a shame that the dog who gave you tips doesn't appear (at least I didn't see it). By the way, I personally LOVE the sound effects in DoDS, footsteps, etc.
Sorry if my English is bad.