A microscope is a good thing but may not always tell you how the stylus sound.
A tangential deck will wear the stylus "sides" slightly more even than a radial deck, that's right,
but having said that, B&O's radial decks are all going very gentle on the stylus and my experience is that the
difference isn't really that huge.
The 2-minute go/no-go test is a record with music that you know very well.
Listen for "s" and "t"-sounds as well as high-hats.
They should sound just like that.
If the stylus is badly worn, they will sound more like a hairspray, flat and un-detailed.
If you can find a record that you also have on f.e. CD, that will allow you to compare even better.
If your daughters ears are better, let her listen and report back to you.
If your cartridge passes the above test it may not be completely worn out but if ears aren't enough, you
will need some repairshop instruments to get all figures exact.
A suitable (and not worn) test record and a distortion meter is good for this.
Martin