That would depend on what you're wanting to do with it. If you wanted to do some free work, like darning or embroidery, you'd probably want one that drops. If you're wanting to do other specialty work that involves special attachments, you'd want one that covers.

One of my machines is an old Singer Touch and Sew, which drops and has a cover.

I have several machines and I can't imagine just having one, since there is no one size fits all. : )

I would think there should be a another machine out there with features you want, but with a feed dog that drops.

Maybe if you post the name of your machine, someone reading may be familiar with it.