I have a reel mower. It's only 16" wide, I wish I had a 22 or 24" width, it would take a lot of time off.
I have a 22" powered mower, and I had previously modified it (aka removed the 'safety bar' around the opening where it shoots out grass). It would always clog when my grass was too long (or slightly damp). I do find that every so often if I let my lawn get away from me, I need to use the regular push mower simply because I don't have enough time (I have spread out my mowing to several days, but there are still lots of other productive things I could be doing), where as I can do my entire lawn in one 45 min sprint with the powered mower which needs only one pass, as opposed to doing double passes (I remow with half the width of my reel mower each way). Also similar weed issue as above, as well as long grass issue.
Properly adjusting your blade makes a HUGE difference. I went from having to do three passes over everything and my wife not being able to see where I mowed, to being able to get away with one pass if I wanted to. My problem is that I usually go 3~4 weeks between mowings.