No, allicorns are just better at magic, the magic in their mind/blood is better than that of a normal unicorn, they have more knowledge and wisdom because of their life span! While twilight becoming an allicorn didnt boost her magic she could still have the same magic power as when she was a unicorn as she wasn't born an alicorn

I think the spark of alicorn magic dwells within every unicorn, but the majority will never learn how to utilize it. I think it's a whole different category. Yes, Twilight's magic hasn't been boosted by her ascension, because I believe she'll have to discover and learn how to use her new powers.

Both of you make good points. Personally, I think that "Alicorn magic" is basically just unicorn magic, and because alicorns have much longer lives, they can learn more advanced spells, as Geass_Pony said. After all, you would think that the new knowledge of this new magic would change you, even just a little, and Twilight hasn't changed a bit. (Though that could be, as Mirage mentioned, because she's just recently been made an alicorn, and has yet to learn her potential.)
There's actually a lot of theories for this subject. It could be that maybe some magic spells just require the user to have wings as well as a horn. I can't say I really know for sure, but these are my thoughts.