Unless you're very tall, nobody posts up like Gary Payton.
I'm sure you will be able to read quite a bit elsewhere on these boards about the character of subwoofers. But you may have inadvertently hit the nail on the head yourself. Your comment about "boom" and the JBL is telling. The best subs provide a more "musical" experience by transmitting the energy faster. The result is what some people refer to as "tighter" bass.
Point being, not all material below 80Hz is created equal. There are octaves of sound down there, and your sub should be able to communicate with clarity and precision, not just "on or off" to the program.
I also like your original post title - it is a good question, and valid for your situation. What can you expect by spending more and replacing your sub? Look at the quality of the driver, the quality and power of the amplifier, the rated frequency response and the quality of build. The Hsu and SVS models are rated "flat" (+/- 3db) down to about 22-25Hz. Is there a similar rating for your current sub? You might be surprised how much program material there is below 35 Hz, especially in movies. If your sub's frequency response drops off rapidly at that point, you're probably missing quite a bit.
You might try to get some material that you are very familiar with, and audition some high quality subs at a local shop just to see whether you can tell the difference between those and your JBL. If you get a "A HA!" from listening to a $800 Paradigm or some such, you would probably enjoy auditioning a Hsu or SVS in your home, which would be the best test of all.
