An engine doesn't necessarily do the same thing every turn. First of all, there are the early turns spent building the engine. Even after it's built, each turn will generally play out differently even if the final outcome (that is, what you gain) is the same. I think the fun thing about engines is that they allow you to take and display control of your deck, and maybe even the game itself (read: pile control). Generally speaking, a fully-functioning engine is a deck that is more powerful than any other deck archetype, and it just feels great that you made that happen and that you can keep it going. After you've got it set up, you play out your engine turn after turn to say, look at this magnificent machine I've created.
Also note that an engine generally allows you to make more decisions each turn, which is the fun thing in most games (consider how "games" like Snakes & Ladders and War aren't very interesting because you don't actually make any decisions in them).
Basic Big Money strategies tend to be less interesting overall since they play out similarly every time, and the turn-to-turn decisions are trivial more often. Yes, I will play this Smithy. Yes, I will play all my Treasures. Yes, I'll buy the Province/Gold/Duchy/Silver. It's usually a lot more scripted and a lot less challenging than engines IMO.
These are generalizations though. There are certainly interesting Big Money games, and there are other deck archetypes besides these two.
