Most aligners have a decent mapping summary log. You could rely on these, or you can try RSeQC's bam_stat.py.

I'm usually not using samtools flagstat, since it is summarising rather alignments not reads.

For comparing different samples, you can use multiQC.

I can't tell you specifically but I find it is a good exercise to read current sequencing publications and see how they present their mapping stats. I am always looking for nicer ways to present boring numbers like that.