I have been a resident of Stockton for the past 24 years. I visited Jacksonville a few years ago, so I do have some perspective of both cities for comparison.
The answer to your question is a matter of personal preference. Let me give you my list of pros and cons. Obviously, my list for Stockton will be much more extensive.
Stockton Pros
Thousands of miles of waterways in the Delta.
Wonderful university setting.
Lively minor league sports scene.
Affordable for California.
Warm summers that cool off in the evening due to the delta breeze.
Ethnically diverse population
Nearby to San Francisco, Yosemite, Sacramento, Lake Tahoe.
Stockton Cons
No major airport in town. Have to drive to Sacramento.
Not a large city, so missing some large city amenities.
Hiking and outdoor trails are limited.
Poor reputation for crime.
Jacksonville Pros
Large city, plenty of big city amenities.
Pro sports - NFL!
Ocean practically in your back yard.
Jacksonville Cons
Humidity...sorry.
Flat land, no mountains anywhere.
Hurricaines
To me, the weather in Jacksonville is enough to turn me off, but then again, I'm a native Californian and couldn't imagine living in Florida's humidity.