As was alluded to in the comments, this really depends. I'm speaking from the perspective of computer science, which on average has a better job market than other disciplines. If you're talking about a research fellowship in very small fields (say, abstract math), you'll probably need to reconsider everything written below.
Successful research fellowships lead to the RF obtaining a number of impactful publications, an additional enthusiastic reference letter writer or two, and a broader research network. They may gain valuable experience writing grants and advising students, which further bolsters their prospects.
If these conditions are met, I'd say that in an average to good job market, such a research fellow is more than %50 likely to obtain a tenure-track faculty position in a reasonable university.
In a bad job market (e.g. the one we had in 2020), these chances decrease dramatically, but still - small, less reputable universities may still be willing to hire a good researcher as an opportunity hire (one that won't be available to them under normal circumstances).
Overall, the chances of a research fellow getting a permanent position are no better than those of a fresh PhD getting one, assuming all else is equal.