Swing-top or crown cap shouldn't make any difference. For each of my batches, I bottle half in swing-tops and half in crown caps with no differences.
Sounds more like your priming sugar didn't get mixed evenly throughout the batch. Did you fill all of one type of bottle and then fill all of the other type? If you priming sugar's not evenly distributed then the first filled could have more and the later less (or vice versa) leading to the uneven carbonation you're seeing.