I definitely think the FJ is in the same ballpark as the H3. On-road, the FJ wins ... but off-road it's all H3.
I test drove 2 FJ Cruisers a couple of weeks ago. The engine pulls strong and the driving position is very comfortable. Lots of headroom, shoulder room and elbow room (similar to the H3), and plenty of room between the gas and brake pedals (more than in the H3).
The H3 feels more solid around corners, has fewer blind spots, and has 4 real doors, but those are the H3's only advantages in town. The FJ kicked its butt in acceleration, passing, and on-highway agility because of its more powerful drivetrain. Both the FJ's 5-spd auto and 6-spd manual shifted smooth as silk.
Even so, I have no doubts about the H3's ability to smoke the FJ offroad. Its stance, clearance, skid plates (FJ's are plastic), wheel travel, torque/crawl ratio and turning radius (despite the FJ's smaller wheelbase) are all superior to the FJ. Once the 2007 H3s come out with the 3.7L I-5, its on-road performance will only improve.
As far as looks go, the H3 wins hands down. The FJ looks like a frikkin eggmobile
I'm definitely getting a 2007 H3.