A 7 is nicer because it has one more gear. This allows you to have a wider gearing range than a 6-speed freewheel, or to have smaller jumps/gaps between gears if you stick with the same range.
A 7-speed freewheel has the sprockets spaced closer together than a 6-speed freewheel, so it's barely wider than a 6-speed freewheel. Will probably work but not for certain.

I have two little-used 7-speed freewheels (both ramped cogs, too) sitting around. A 13-28 SunRace (nearly new) and a 14-28 made by Shimano (only a few hundred miles). Both of them have only been used with new chains and the teeth aren't worn out at all. I'd part with either for about $15. PM me if you're interested. Cheaper than buying a new freewheel, and just as good.