A couple of comments:
1) If you want to see if the Activator you have is sufficiently wide, you need to get some magnetic viewing paper. This is a pair of transparent pieces of plastic bound together with oil between them. Fine iron filings are suspended in the oil. When you hold the viewing paper over the top of the pickup, you'll see an image of the magnetic structure of the pickup appear. You can get this at a kid's science supply store or you can buy one from EMG (I'll admit right now that I've never seen one in a science store before and it no longer appears on EMG's website, but I'm sure you can order one by calling their customer support line).
You want the magnetic structure to cover the full width of your strings plus a little more so the entire range of excursion of the string is over the magnets. You want to check this with the pickup installed too. Some pickups have guts much smaller than than the cover would make them appear and they're not always centered under the top. If you don't have full coverage of the string excursion by the magnets, your outer strings will definitely sound gutless. It makes a HUGE difference! This is partly why a Fender pickups have 8 polepieces - it widens the magnetic field so you don't get volume fluctuations when the string is swinging. The original P-bass had only 4 polepieces and the strong transient fried a lot of those ancient old bass amps.
2) The Fender Jazz basses produced in Mexico also use the bridge pickup in both positions, so this is a common cost cutting measure these days. The Mexi Jazz has pole pieces instead of bars, so it's really non-optimal but saves them a couple of pennies in production since they don't need to stock two different pickup models.
3) Having the same pickup saves Fender (and presumably Carvin) a couple pennies but it is at a cost to the player. Leo was a pretty darn clever guy when he first started building these things. The Jazz Bass pickups are single coil which is simpler to make and has extended high end compared to a humbucker. But they pick up a lot of buzz and hum. So, on the Jazz, Leo inverted the magnets on one of the pickups and wound it in the opposite direction. Without getting all nerdy on you, the result of doing this is that you get the full single-coil tone from the pickups but when both pickups are on, the hum is cancelled out just like a humbucker. If you use the same pickup in both positions, the tone will sound the same, but there will be no hum cancellation.
I believe the Activators (and EMGs too) are a stacked humbucker so they'll be quiet at all times. On a regular Jazz with the trick pickups, it is quiet when both pickups are on but will buzz when you use just the neck or bridge.
Incidentally, the two halves of the P-bass pickup use the same trick which is why they don't hum but are still pretty bright.
The coolest implementation of eliminating hum is (not suprisingly) on the Series bass, where there's that third dummy coil mounted flush between the two pickups. It has a precisely wound coil but no magnets and exists only to cancel the noise from the Series single coil pickups. This is the most expensive way to do it, but this gives you that beautiful pure single coil tone with no noise and it works with any combination of pickups.
David Fung
