First of all, let me say that tone will always be subjective, especially when discussing the rather subtle differences you get with different tubes. If you're happy with the tone you get with your current tubes, that's what you should stick with.
Now for MY opinion on JJs:
JJ have several different types of 12AX7. You didn't specify which ones you're using.
The most commonly seen type is the JJ ECC83S so I'll assume these are the ones you're using.
The JJ ECC83S is in my opinion a rather muddy sounding tube with poor low/high frequency extension. I also find that they test weaker than most other 12AX7s when new and often go fast downhill from there. The only good use I've personally ever found for this tube is to soften the tone of overly bright guitar amps.
For my taste, pretty much any other 12AX7/ECC83 will be better. At least tonally.
There's also microphonics and ruggedness to consider of course, and in this respect the JJ ECC83S is at least better than average (for current production tubes anyway). This makes it a relatively safe choice for gigging/touring.
In contrast, JJ's long plate 12AX7 (the ECC803S) is tonally FAR superior in my opinion, but also far more prone to microphonics. This makes it a poor choice for giggin/touring.
Also, unless you buy JJs tested/matched by a re-brander and base any comparisons on whatever arbitrary scale they use, it doesn't really make sense to make any assumptions about gain or noise levels. They can be all over the place in my experience, not very consistent. The quality control (that in the golden age of tube manufacturing used to happen at the factory) is now left to the re-brander or the end-user. Tube factories today ship out tubes that are WAY out of spec. Of course, Aspen Pittman (Groove Tubes) is to blame for this, after he somehow managed to convince guitar players that selling out-of-spec tubes was a feature rather than just a way to get rid of tubes that in the past wouldn't have passed QC. Then everyone else soon realized that they could also get rid of all those out-of-spec tubes in the back, by selling them as lower/higher graded tubes.
Anyway...
If your amp is mainly for gigs/touring, I would just stick with whatever you've got. Those are cheap tubes that can be easily replaced if they break from transport or heavy use. We are after all talking about relatively minor tonal differences. At least in the context of a live gig.
If the amp is mainly for recording.... Well, that's where I would seriously consider some decent NOS preamp/driver tubes, to bring out those last 10% of tonal bliss from that amp (NOS output tubes are sadly not a realistic option at this point).
NOS 12AU7s are still readily available at reasonable prices. That's a no-brainer really.
NOS 12AX7s are a different matter. They have become outrageously expensive, but there are still SOME bargains to be found.
Early 60s GE 12AX7 long/grey plates are superb in bass amps and can still be found at more reasonable (or at least less insane) prices than other NOS tubes, because they're not popular among guitarists and the hifi-crowd. The reason for this is the slightly rolled off highs you get with the early 60s GE longplate, but this won't matter at all in a bass amp.
If you wanna go nuts with NOS there's nothing I've found that beats a late 50s Mullard long plate ECC83 in bass amps. These are GLORIOUS sounding tubes in bass amps (and any other amps for that matter). But I honestly wouldn't bother at the prices these late 50s Mullards sell for these days. You could buy an entire amp for the same price...
And of course, most of the 12AX7s that are sold as NOS today aren't really NOS, but used tubes, and in many cases very worn or even faulty. Buyer beware! 12AU7s are much safer to buy NOS. They're usually still actual NOS tubes in original packaging.