Would recommend Mexico (Mayan Riviera area like the area around Playa or Tulum) or Belize. I've spent a lot of time in both, so it really depends on what you want. I opened up an office in BZ three years ago and go there frequently. The Mayan Riviera is also my primary vacation (relax) destination.
Fishing - both are good. Boats are easy to come by anywhere up and down the Mayan Riviera, as well as off the nicer areas in Belize (Ambergris Caye / San Pedro, Caye Caulker, Placencia). I know a captain (use that term loosely) in BZ, as well as several smaller islands you can wade right out and fish. Several islands and resorts cater specifically to fisherman, but still nice enough you can bring the lady.
Resorts - MX wins this category hands down. Service and price are places BZ is sorely lacking. You can get a pretty darn nice all inclusive package including flights to the Mayan Riviera for great prices. I do know some very nice places in BZ, but they are more expensive, not near as luxurious as MX, and the service does not come close unless you want to spend a boat load. Also, BZ offers very little in the space of all-inclusive resorts. The few that do, are lacking.
Crime - The Mayan Riviera area is a lot better than people think so long as you don't go where you shouldn't. Belize is worse than people think. Overall they are about the same. Theft is probably a little worse in BZ, but BZ is probably a little less violent. Police are corrupt in both areas.
Adventure - both are good. BZ has islands, jungles, Mayan ruins, fishing, etc.. The Mayan Riviera has the same, but better ruins.
Beaches
Hands down MX here too. You will not find a true beach near Belize City. The beaches on the Cayes and in Placencia are OK, but they are typically filled with sea grass etc... Not bad at all, just not comparable to the MR.
Overall both are great destinations. If you don't want to break the bank and have really nice accommodations, will do a little fishing, and little ruin site seeing, a trip to Cozumel, etc.. the Mayan Riviera is probably the best bet. If you want to spend a bit more, go somewhere a bit more raw, not over concerned about resorts, and value fishing over comfort, BZ is probably the place.
If you are interested in BZ or MR, let me know and I can help with either. I've got a lot of friends and contacts in BZ. Also, if you want to share your budget, I can point you towards the best places in either area.
One of the best sites in general if looking for a rental villa or beachfront house.
Luxury Villa Rentals & Vacation Rentals | Travel Keys
Favorite place in MR handsdown
El Dorado Maroma | Riviera Maya Resorts | Karisma Hotels & Resorts
Couple of my favorite places in BZ
Palapa Bar & Grill
Ambergris Caye Resorts | Belize Condo Rentals - San Pedro | Wedding Packages | Honeymoon - Grand Caribe Belize Resort & Condos
Private Island Belize Resorts, Luxury Island Vacations | Cayo Espanto Resort
Belize Private Island Vacations | Robert’s Caye Belize | Ranguana Caye Belize | Placencia Belize Beach Resort – Robert’s Grove
Belize Resort on Ambergris Caye