Obviously "it depends", but I would say that in general, no, you shouldn't sacrifice that Province for a Lab. Adjusting your strategy to the hands you get is a pretty big part of becoming a better player, in my experience. Sometimes you get early game draws that push you toward big money (Silver+4Copper followed by 3Copper+2Estate on turns 3 and 4 rather than that $5/$4 split for Laboratory and Caravan, or whatever, then turn 5 is Estate+3Copper+Gold, turn 6 Silver+4Copper, sweet!), and a "lucky" BM deck is often pretty strong (on Province boards). It surprised me when you mentioned the Lab deck crushing you in the endgame; I'd quite have liked your side of it with the information available!
Like in the game we played earlier today where I was planning on picking up a Library on $5 but never got around to it, I feel it would be a pretty big mistake to pass up a Gold/Bank/Platinum for it. Of course, sometimes that $5 card is incredibly strong (hello Witch) and there's not much question about it, but most Library/Laboratory type situations, I'm grabbing that Gold probably.
More often than not on engine'y boards, it's like, the best option would be engine card #1 and engine card #2, but when you get the $6/$3 split, Gold/Silver might be better than engine card #1 and Silver (or engine card #3), so in a sense you've been unlucky in that you can't pursue the strongest strategy, but not adjusting to the more BMesque approach and still going for the (worse) engine will cost you.