Can you post the commands you used for both featureCounts and htseq and the summary statistics they produce?
For one thing, the two programs have different defaults for filtering reads on mapping quality.
-Q <int> The minimum mapping quality score a read must satisfy in order to be counted. For paired-end reads, at least one end should satisfy this criteria. 0 by default.
-a <minaqual>, --a=<minaqual> Skip all reads with MAPQ alignment quality lower than the given minimum value (default: 10). MAPQ is the 5th column of a SAM/BAM file and its usage depends on the software used to map the reads.
Once I compared to two and found negligible differences but I can't remember exactly how I made the comparison.