Definitely the original which I consider to be the greatest cast album ever made. The performances are thrilling and it's complete. It even includes a large portion of the dialogue. It's Sondheim at his greatest.
After that, I also quite like the recording of the Doyle production. It's not complete and the orchestra sounds very thin due to the actors doubling as the orchestra, but the performances are sensational, especially Lupone and Cerveris. Lupone is actually my favorite Lovett (I know, blasphemous). I also adored the radically re-imagined production as well, which might contribute to my enjoyment of it.
The movie soundtrack is positively atrocious, just like the film. Depp and Carter are so terrible that I can't even put into words how ghastly they are. They're shrill and their acting is terrible. Just the f*cking worst. An embarrassment to musical theatre. Why couldn't they have gone with someone like Hugh Jackman and Meryl Streep? Neither are perfect singers, but their voices at least fit the parts and they can actually act!
There was also the 2012 london recording I believe. Imelda Staunton is great and Michael Ball does a nice job in the part and makes his tenor voice work very nicely in the part. The recording just sounds a bit thin though due to some modern recording techniques and it is very incomplete.
BUT, the best Sweeney Todd isn't even on a studio recording! George Hearn sings his a$$ off in the 1982 video recording. His classical voice sounds like warm butter. Warm goddamn butter! His acting is positively manical and brilliant on top of it all.
The recent recording from Lincoln Center is decent. Emma Thompson is great as is Audra Mcdonald, but Bryn Terfel falls flat for me. His voice is overly operatic to the point of being distracting and his diction is horrible muddled. I won't even get into his acting, which is virtually non-existent. The production is also heavy handed and poorly executed, IMO.
Stick with the OBC. It's definitely the best.