I work for a Meat company, in the division that sells to restaurants. Although I'm not a " meat cutter" I know a bit about this.
First, age makes a difference. In Canada most grocery stores steaks and roasts are aged 14, maybe 21 days. 30 - 45 days under carefully controlled conditions is way better.
"Wet " aging, in the vacuum sealed bag from the slaughter plant will improve tenderness, and to some degree flavor.
"Dry" aging. Aging in an unsealed state allows moisture to evaporate. This process not only improves tenderness, but intensifies flavor. It does however give microscopic critters an opportunity to set up camp on your future meal.
Before attempting to age something at home, one should be certain what the "kill date" is. A place like Costco where you can buy a whole Striploin, Ribeye, or whatever sealed in the bag it came in will be able to tell you this. A grocery store with a smaller portion plastic wrapped on a foam tray,,, I'd be careful. It may not even have been cut and packaged in that store, or that city for that matter. It may have been previously frozen. If there are people cutting meat in the store, talk to them.
The beef we sell or cut into steaks is aged in a closely monitored area, there are alarms that sound if the temp varies + or - 1 degree Celsius.
A domestic refrigerator in a kitchen in the summertime. where the door is open many times per day the temp can vary wildly. Keep that in mind. If you have a second, less used fridge that would be better.
Aging beef makes a big difference in eating quality. If it didn't we wouldn't tie up hundreds of thousands of dollars in inventory for weeks at a time. If you do it at home, know how much age is on the product you start with, be careful, read lots about how to do it. Most of all, if you give it a whirl and it smells rotten be prepared to pitch it. A good steak or roast is a beautiful thing, but it ain't worth getting sick, or dying for. Christmas dinner can be pretty awkward if you killed a few family members on the labour day cook out.