How crucial are banking apps? Your experience with them vs. browser banking?

Banking apps seem to be a motif among things that don't play well with privacy ROMs. My bank's website does everything I could want out of it. I think I might be ignorant to something.

• What about banking apps is especially compelling?
• How often do banks put must-have features behind an app?
• And should I be concerned that banks might move away from offering services through browsers?