Both things you linked are 3-jaw metal lathe chucks, not suitable for turning wood. (I mean you can try to, and people did before we had wood lathe chucks, but why?) Doesn't have anything to do with the size, it's simply not the right tool for the job.

It won't hold the work nearly as well as a four jaw wood lathe chuck like this:

https://www.amazon.com/Nova-Premier-Woodworm-accessories-reversible/dp/B08M8W77QQ