I've been wondering about good reel mowers too. I've been using a
5-blade Craftsman for many years. It's OK but has shortcomings.

I was just about to buy an electric rotary, but with their drawbacks,
I'm considering a better reel mower.

From what I gather, 7 blade mowers are better than 5. Apparently also,
better mowers don't have scissors-like contact between the blade and
whatever the blade has contact with. Apparently this lack of contact
makes Brill mowers easier to push, and need little sharpening. Quieter
too, not that noise is an issue either way.
http://peoplepoweredmachines.com/brill_luxus.htm

I also see Mclane mowers that have the reel as wide as the wheel width,
which should eliminate the annoying "can't mow near the edges" feature
of reel mowers. But a review I read talked of needing to sharpen it.
See the bottom mower on this page. They only seem to have photos of the
powered ones.
http://www.mclanemower.com/reelmowers.asp

Will a good reel mower cut the type of grass that doesn't grow
vertically? Mine doesn't do it very well.

Will it cut stalks that shoot up from the lawn? Mine won't.

Anybody here have sucess with difficult grass with a reel mower?