As I said, my veiw is that Cadance is a demi-alicorn and that she
does have the powers of all three types of pony at a greater level than ordinary ponies (planetary level),
does age slower than ordinary ponies (about ten times slower) and has power over a concept (love in her case). Full alicorns like Celestia and Luna are
even more powerful and age
even slower.
I call the alicorn of Hearts and Hooves Day Princess Cornucopia and consider her to have been the alicorn of harvests and was associated with Saturn, just as Cadance is associated with Venus. Previous alicorns of Venus have included: Venus, Cupid, Eros, Morning Star, Imperatrix, Aphrodite, etc.
Chrysalis is the equivalent of an alicorn (specifically, their highest ranking alicorn) for the changelings and every sapient race has their own equivalent.
But this is all just my headcanon.