They're both exploiting the same principal. It's more efficient to generate thrust by accelerating a large amount of air a little than a little amount of a air a lot.

Figure of merit is the bypass ratio. Props are 50-100, fans are 3-10.

So big advantage of a turboprop is a much higher bypass ratio than fans. Downside is props can't spin as fast and so need a high speed gearbox to drive them. And props loose efficiency at high speeds.

I think for large fast aircraft turbofans are a win. For medium sized slower aircraft turboprops are a win.