Adobe Flash is a lot more sophisticated with regards to animation, which is one of its primary functions. You can output as flash/html5/or as a .gif
After effects is also a sophisticated option although as it's primarily for motion graphics for video rather than web, so perhaps overkill.
Photoshop is good for image optimisation, but clearly inferior for animation with regards to the tools available for that task which are very minimal. As such, in no way could it ever be described as the 'best software for creating animated banners'.