Not sure if it would be possible, I'm not very familiar with how codes / designs work, but it would be awesome to see it converted into a mixture of offices/hotel/condo/apartments/reopen the rooftop restaurant. It's really not a bad location for all of those and it would help spark the re-use of the old, old JEA building behind Sweet Pete's IMO.
Also, as someone who lived in downtown Jax for almost 5 years and has lived in / near downtown Orlando the last 3 years, it's definitely the density and "newness" that makes Orlando's downtown better. As Lake said, most of the highrises are barely 10-20 years old and many of them are mixed use. Downtown Orlando also feels a lot cleaner than downtown Jax. I think it's a combination of the pocket parks and greenery hanging from the light posts. There's just as many hobo's hobbling around here, but since there are so many more people living in a smaller space you don't notice/feel unsafe because you're never alone. 55 W, Cobb Plaza, Solair, Post Parkside, Paramount On Lake Eola, and Aspire are just SOME of the mixed use highrises here. They all have a mix of ground level shops, bars, businesses, restaurants, PUBLIX, CVS, etc. And there are cranes constantly putting in new mid/high rises. Seriously, I can't even count how many new buildings have gone up just in the last 3 years and there's no sign of it stopping. UCF is about to start work on a massive campus expansion downtown, a new SunRail/multimodal hub is being designed, and this is about to start construction. http://www.lpcsoutheast.com/properties/tremont-plaza/
Unlike Jacksonville, nearly all of the highrises have shops, restaurants, bars and businesses on the ground floor. When you walk around downtown Orlando at any given time, day or night, you see people patronizing these places. In the time I lived downtown Jacksonville I would run and ride my bike nearly everyday. I liked exploring new areas. But man, everywhere always seems dead. Even in the day time. Riverplace blvd is a prime example of a spot that doesn't exist in Downtown Orlando. You have the cities premier public spaces there (Riverwalk, Friendship Fountain, Treaty Park, MoSH, Apartments, Offices, Hotels, etc), but nothing is on the ground level so you rarely see anyone. Even the vagrants don't walk around there.
Long rant short, until Jacksonville starts embracing mixed use buildings and enforcing new buildings/renovated highrises to create public ground level spaces it will never thrive. Yes, we need more places to live, but from what I've seen even the new apartments that are going in next to the Court house and Convention center completely ignore the sidewalks and the city isn't doing anything about it. Hopefully once the density picks up a little more they put their heels down...