So the theory is that 1:1 is closer to the concentration of nectar, and thus may stimulate the bees to do all the things they would normally do during a nectar flow, build comb, raise brood, etc., hence the typical recommendation for 1:1 in the spring. 2:1 is much thicker than nectar, and so it puts the bees more into a "robbing" frame of mind, where they are just rapidly storing it instead of consuming it, plus it's easier for the bees to dry and cap, hence the recommendation for 2:1 in the fall. As I said, that's the
theory; whether that's the
truth is another matter.
I've heard lots of different opinions from lots of different beekeepers, and I'm inclined to think that the ratio doesn't really matter. The bees will likely do whatever the season dictates that they do, regardless of the concentration of the syrup they are being fed. The addition of food could keep a colony active and growing during a dearth, but I doubt the syrup strength itself factors in much in that case. The only thing that would be a serious concern, imo, is having a lot of uncapped syrup in the colony going into winter.
I don't have much experience feeding syrup. I fed my packages 1:1 when I first got bees, and I also fed 1:1 one spring when our early nectar flow was wiped out by the late frost. I used to feed 2:1 to colonies who were light going into winter, but for the past few years I've had enough extra honey to just donate a few frames to colonies who are in need. My winters are too cold to feed liquid syrup, so I do make sugar balls (12 parts sugar to 1 part water makes the sugar the consistency of wet sand, pack into balls, and air dry on a cooling rack) as emergency winter feed, and there are usually one or two colonies that need them after the calendar turns.