There's a lot of differences between the Series I and Series II, but you won't hear that much difference in sound. I had my newest Series built in the early 90's so there's defintiely differences now, but I think it's fairly close.
Series I and Series II have the same core electronics (same pickups, same EQ board). In addition to the Series I stuff, Series II adds a master volume knob and has CVQ knobs instead of the Q switches. Internally, the Q switch selects three different resistors to set up the EQ curve; the CVQ replaces those three resistor choices with a continuously and infinitely variable pot. You may like one or the other better (CVQ has more choices, but is not very repeatable compared to Q).
The woodwork on Series II is fancier with more laminates everywhere. The neck usually has more structural pieces and usually has additional pinstripe laminates as well. Same thing goes for the body, where there are at least pinstripe laminations between the top, core, and back and often multiple pinstripes. Certain configurations and body styles may have different setups at from the factory (wide neck basses often have more structural laminates, and I think the often make a call on the pinstripe veneers based on how the pieces of wood look together). Of course, all this stuff is customizable when you're ordering a new bass.
One very noticeable difference is that Series II normally comes with LED side markers which power up when you use the external power supply.
I'm not sure that they still do this, but back in the 90's, all the hardware on the Series II was 18K gold plated - the back plates, bridge, sustain block, even the little screws that hold the back plate on. Series I was normally done in brushed brass.
I don't know about some of the newer stuff like the inlayed logo.
David Fung