I think it's more a matter of approach than gear necessarily. There are lots of ways to get there, but some general things to try:
1. most likely want to use a pick, but experimenting with finger technique and placement can help too
2. go for round-wound strings, stainless steel strings will do a lot to brighten up an otherwise dark sounding bass. rotosound swing '66 is a perfect starting point
3. experiment with EQ - playing around with upper mids and treble can lead you to some interesting things
4. experiment with hand position when you play... playing closer to the bridge will tend to give you more of a midrange tone, which can accenuate melodic playing
5. experiment with how hard you play - playing harder with a pick will accent the attack, which is a lot of what you hear from those bass players
6. experiment with light overdrive - a lot of brighter bass tones can benefit from some judicious grit to add harmonic richness
7. experiment with your pickups - if you're playing a 2 pickup bass, dialing in the bridge pickup is likely to add some brightness to your tone. a favorite setting of mine on 2 pickup basses is to set the bridge pup on full, and roll the neck pickup to about 80%, this typically brings out the midrange quite a bit and increases presence
8. speaking of presence, if your amp has a presence knob, try messing around with that. it's typically another name for hi-mids, and will change the feel of the attack as well as (of course) the actual presence
9. play with preamps or preamp pedals - a sansamp or similar (VT Bass; even the behringer clone) can get you into this territory very quickly as soon as you boost the gain and treble. a friend of mine plays an Aria hollowbody and uses relatively extreme settings on a sansamp to get an amazing postpunk tone... bright, gritty, but thick. he leads his band through every song with a forceful tone that sounds right up your alley.
and most importantly:
10. FIND YOUR OWN WAY. what you'll quickly realize if you were to do all of the above... you'd have a thin, sickly, clanky, overbright bass tone that probably wouldn't work in most settings. a lot of what goes into making this particular sound work is finding the right balance. Peter Hook balanced his technique of playing a lot of high notes by using the heaviest gauge strings he could find, which added a weight to notes that might otherwise sound thin. the whole thing is a balancing act: you might try using some brighter strings, and then find that you want to play up closer to the neck so as not to go TOO far into the mid-forward clanky stuff. personally i play a bright bass (rickenbacker) with a pick, but use nickel roundwounds, play closer to the neck, use a VT bass as well as the tube drive on my ashdown head thru a tweeterless Orange 1x15 cab... basically balancing a brighter approach with other choices that thicken up the tone a bit. best advice is to experiment and have fun!
