While I own the ASW-10 and it's a great sub at it's asking price Matt34 is correct in that you would be making a lateral move. To get real improvement you need to upgrade to something like the Cadence CSX-12, HSU STF-2 or above.
The TSC has good output but nothing to amazing. It goes down to 28hz but does not have huge output. 32hz is where the output picks up. For its asking price its a big improvement over the crappy Sony and Polk PSW subs. The real nice thing about the ASW-10 is the bass it does produce is very clean and controlled. It's not sloppy or booming like most 150.00 subs.
Your JBL is a good sub. Its just sensitive to placement and needs attention paid to it's set up. The eD parametric eq for 100.00 would be a better upgrade for your JBL than the ASW. This is my next upgrade along with the Auralex SubDude since I have wood floors under the carpet and need some isolation from the floor.
Hope this helps.