I've never used SR but had Chorus on my road bike the past 3 years and also use DA7900 on my CX bike and now DA9000 on a new road bike. I really liked the multi-shift on Chorus but maybe just because it sounded cool clunking through 4 gears at the crest of a hill...At the same time, I've probably accidentally shifted two gears instead of 1 more times than I actually needed multi gears. I think I can get through DA gears just as quick with quick taps on the little lever. DA has a smoother, less mechanical shifting action which can be nice but at times it's almost too light.
My experience is exactly the same as yours. I appreciate the multiple dumping of gears especially as I'm changing on the front derailleur to compensate for the change, but it's also reasonably often that I accidentally go two shifts up when I only intend one. I have not tried any of the Powershift levers which only allow one downshift at a time, but I cannot imagine it being much of a compromise for me, especially with the newer Potenza/Veloce levers having the lower thumb position.
Because the Shimano levers have quite a light action for the downshift on the right lever, doing a few short clicks has never bothered me.