I completed mine a couple weeks ago, and did the online application. I actually didn't know about it before I took the class (I've had the HCP before, figured it was still a paper thing), but he told me about the online app, and on one of the breaks during the class portion he let me in his office to do on his computer. Didn't know it was this new though.
App is online, carry permit class pass/fail status is updated online. Still have to make DMV visit to show birth certificate/take picture/pay fee, then go online or call to schedule appt for fingerprints. I did DMV and fingerprints on the same day, background check completed and application approved in 8 days, 6 days after that received permit, so 14 days total, including weekends. Lot faster than last time I did it a few years back, back then they really pushed the 90 day limit. That was a long wait.
As for benefits, well for one you can also use the same page to check the status of the application.