Hens are smaller, usually 12 pounds and under. Toms are larger,usually 16 pounds and up.
Some people say the hen is more tender. Some people say the tom has more flavor. In a mass produced turkey I don't think either of those statements is supportable.
I usually cook one of each. I cook the hen about a month before to play with any new recipe or technique AND TO MAKE TURKEY STOCK. I freeze the stock for Thanksgiving. Having good turkey stock on hand for the big day really improves what you make for Thanksgiving.
Your mother in law is correct. Since toms have a larger breast bulk they would in fact yield more white meat. Dark meat today is getting harder and harder to find both in chickens and turkey. Next time you cook a bird notice that the dark meat is getting lighter in color. This seems to be based on the feed they are useing. Most people prefer white meat so the breeders are trying to accomidate them.