I have had the same experience. I found the other problem with only playing sitting down (apart from what the others have said) is that when you are sitting down the guitar is anchored pretty firmly in place by your picking arm and your legs. This is not the case when standing up.

So as a consequence to only playing sitting down you develop the bad habit of being too rigid. When you stand up the guitar seems to swing around uncontrollably. It's kind of like bobbing for apples - you make the adjustments you are used to doing in the sitting position and you just can't keep the guitar still. I have found by concentrating on not pushing down with your picking arm the guitar will come to rest. But don't raise your shoulder or it will get sore.

Also, when you are picking take a look at what the headstock of the guitar is doing. Is it bouncing around? If it is then you are pushing too much with your picking arm or fingering too firmly. Have a look at the great guitarists play when you have a chance. They keep the guitar dead still. It looks like they have it on an invisible stand or something. This is what I try to cultivate in my playing.