Good, but as good as the original
Never having seen the Sondheim musical, I cannot really tell you how this film compares. I can however tell you that it is sure to please fans of the ongoing Burton/Depp film collaborations. You get another suitably weird and creepy Johnny Depp character set against the visually Gothic Revival style Burton is so well known for.
Nor is the total lack of singing ability on the part of Mr. Depp a weakness here. Indeed the fact that he doesn't sing very pretty, kind of more the way a barber and not a trained tenor would sing is if anything a point in the films' favor.
Ultimately, however, this is neither one of the best films Depp has made, nor one of the best Burton has made, nor even one of the best they've made together.
Check out the original 1936 UK Sweeney Todd for a more authentically Cockney version without the cheesy songs.