The alternative is not StringTie vs featureCounts, but either Salmon or RSEM vs featureCounts. StringTie is run in addition, to potentially detect novel transcripts.
Why Salmon (or RSEM) rather than featureCounts? Because featureCounts is not very sophisticated and throws away all multimapped reads by default (or it double-counts them if you choose, which is not any better). Salmon/RSEM, on the other hand, distributes counts of multimappers among the loci by probability, which means that the counts may be slightly wrong, but at least not totally lost. (The resulting non-integer counts can be rounded, if necessary.)
Depending on the cancer, the most common "nonstandard" transcripts could be from fusions. If that is something you are interested in, there is #CGB1CL0SC. For finding various splicing variants, have a look at #C0493FQQZ3P.