(any relation to the Flinstones' cute pet? :)
My personal issues with upper apt noise revolves around squeaking and creaking, more than shoes thumping. Carpet or no carpet there was always noise downstairs so first identify the noise.
When you pull the carpet work on screwing down the subfloor, etc.
At one building the upper apt had pad + fuzzy carpet + another layer of fuzzy carpet. It was an inch thick! The downstairs folks STILL complained. I think it will ALWAYS be something to complain about.
Note to self: only rent downstairs apts to the hard of hearing.
I also tell the upper res this is a "shoes off" apt. Helps a little.
Carpet is a stink and allergen holder, plus the cost of cleaning at turnover.
We have gone to smooth LVT floor (Luxury vinyl tile laid on a super smooth surface) and some throw rugs. A runner in the hall, area rug near the bed, etc. CHEAPER to replace than to have cleaned. You only need carpet where they walk, not wall to wall or under the bed and sofa.
There are LVT products with a a built in foam backer. That should help.
This may sound crazy but it works...in lower priced homes we lay clean, pretty luan, factory edges only, stapled neatly, poly coating. Looks good, somewhat durable, easy to replace, gives a smooth underlayment for rugs and future LVT.
Hope that helps!