Spider-Man 2 was, admittedly, improved over the first film thanks to a good score piece for the villian (which Goblin never got) and the addition of said piece along with more chanting into the opening credits sequence. Even the use of the Hellraiser music that they bought was good. However, in the end, it follows the footsteps of the first film in that it's largely unmemorable and generic. Spide himself lacks a good theme, which even Daredevil managed to get.
The Punisher's music is haunting and sad, yet also militaristic. It has the perfect mix of a Western "cowboy" tone with that of a soldier - which is ideal for the character. It also knows how to back off during the action and when to insert a little percussion. Its only failing in my eyes is that it gets much weaker and more generic during the sequences without Frank on-screen - stuff that deals with the Saints, for example, doesn't really have any good music in it.
In the end, however, The Punisher is the more appropriate and more memorable score. Spider-Man 2 is just too uninspired.
