Mobile Apps are Faster Than Websites
Depends on how optimized mobile apps and websites.
Personalized content
IIRC it's expensive to create personalized service, besides there aren't many thread / thread bumps everyday so users simply can see recently created or bumped thread by themselves.
Instant Online and Offline access
Websites also can have similar feature (offline access)
Using device features
Access camera and gallery might be handy, but other features not really useful.
Push Notifications
Instant updates
Maybe, but this forum currently only have "Show unread posts since last visit" and "Show new replies to your posts" which IMO isn't really useful.