You're likely observing a few different things. Firstly, hg19 has a number of problematic regions that cause aberrant alignments. These were largely fixed in hg38, which is one of the reasons people have transitioned to it. The other thing you're observing is that using different numbers and sizes of genes will result in different counts and thus different filtering and results from multiple testing adjustments.
For what it's worth, there is never a reason to use cufflinks any more. The authors don't even recommend using it. There's rarely a benefit to using stringTie in human data.