All signs point to reels getting the most reach right now, on both Facebook and Instagram. Meta has put so much of a focus on vertical video/reels that you are best off just posting all videos as reels.
However, keep in mind this is just from a reach/impressions perspective. Many users have said their impressions skyrocket but their engagement rate goes way down. I think this is due to Meta pushing their reels on so many people that you end up with viewers who don’t really want to watch your content. The average view time is also really low, so it has become challenging to back up the “just post reels” claim.
I don’t think there’s necessarily any downside to posting video to both reels and pages. But your top fans will be delivered redundant content and that could lead to losing followers if you make it a common practice.
Finally, just remember to create and post videos that are truly valuable. I’ve seen so many reels recently that just do it for the algorithm, and they’re complete crap. Keep inspiring, educating, or motivating with your content and the engagements will follow!