You came to a hummer forum to see if you should get a Jeep
Here are some differences I see between the 2007 JK vs the 2007 H3. I own an H3 but haven't driven a JK, so this is all from the specs. I didn't list the things they have in common and probably missed some.
Off road
JK Ultd Rubicon ... solid front axle, electronic sway bar disconnect, locking front diff, longer wheelbase (may help climbing), more ground clearance, better approach & departure angles, removable doors, removable top
H3 Adventure ... bigger stock tires, better breakover angle, smaller turn diameter, wider track, more low end torque
On road
JK ... lighter weight, longer wheelbase (high speed stability?)
H3 ... IFS, more HP throughout RPM range, more low-end torque, (slightly) more high end torque, low road noise, longer range (same mpg, bigger gas tank)
Utility
JK ... more interior volume (partly impeded by roll cage)
H3 ... more payload, more towing capacity
Luxury
JK ... (don't know)
H3 ... power sunroof, many interior choices - including leather, monsoon sound system, lots of chrome options
Safety
JK ... roll cage
H3 ... rear side curtain airbags