The US has a higher attention to detail, but the Tributes are no slouch. The US ones get you a lot more options, though, with colors, woods, neck profiles, etc.
The Tributes use US pickups and functionally equivalent electronics, so they sound pretty close.
The big difference is that the older ones (1999 and prior) have what is nicknamed OMG mode instead of the current series mode. This is a thicker, bassier tone than the current series, which is a little more mid present and in your face. Parallel modes are essentially the same, though I did think my ‘00 was a little brighter than my ‘89 when compared directly. Wouldn’t notice it in a mix.
Yes, you can use without a battery. The controls are all passive and the preamp is more or less a buffer that you can switch on.
From the neck, the switches are pickup select (N / N+B / B); Series/Parallel; Preamp Off/On/On with treble boost.
Series/Parallel is how the two coils in each humbucker interact with each other. In series, the signal from one coil feeds into the next where in parallel, they run in tandem beside each other. Series is louder and thicker.
As I mentioned before, the preamp is basically a buffer or linear booster. The treble boost setting just gives a little more boost in the top end.
Pots are master volume, treble cut, bass cut.