DISCLAIMER: The following represents my opinions formulated after recording and playing tests I've done between these two brands of pickups. In no way am I suggesting one set is superior over the other or that another set will be exactly the best tone for every playing situation. However, there are real differences between the tonal qualities of these two sets of pickups.

Introduction
This comparison was made with a variety of pickup settings, in both live and recording sessions. The Seymour Duncan pickups (SD) tested are their Basslines Music Man Stainless-Steel and Jazz bass passive replacement pickups. The Bartolinis (BT) are custom wound Music Man and Jazz bass type passive pickups. Both sets of pickups were mounted in identical Lakland 55-94 basses with Bartolini active 3 band onboard pre-amps. See the notes below for the reference amplification and recording systems used. Note that on all the testing no EQ was engaged on the onboard pre-amp.

Setting #1: Bridge and Neck Pickups blended 50/50
The first thing I noticed was that the BTs have a lower output than the SDs. This is not a bad thing - in fact the SDs were so hot that I had to roll back the volume to stop overdriving the Demeter pre-amp when plugged into the high gain input. From there I had the immediate impression that the SDs had more of the sort of "twang" that I associate with a typical Music Man (MM) than the BTs did. I would characterize the SDs as having more of a naturally occurring scooped or "smiley face" EQ. This reinforces the comparison to the well known MM sound. Due to this, the SDs seemed to lack what I would call warmth in the midrange, which the BTs certainly did have.

Setting #2: Bridge pickup alone
The BT didn't seem to have quite the low end response as the SD did. In addition the SD delivered some aggressive high end that seemed to be absent in the BT. At the same time, the BT possessed more personality or character than the SD, largely due a more developed midrange that was lacking in the SD. This impression was roughly the same as when the pickups were in the 50/50 blend setting. Note that much of the missing midrange in the SD could be dialed in with the on-board EQ.

Setting #3: Neck pickup alone
Both pickups produced the sound I associate with a typical Jazz bass neck pickup - lots of deep low end with plenty of fundamental bottom end and general mellowness. Having said that, the BT seemed to have less of an active sort of tone with a more natural presence - even though both the SD and the BT are passive pickups. I'd have to say the BT produced a less processed tone closer to a standard Jazz bass neck position tone than the SD.

Overall Impressions
As I was completing the live comparison of these pickups, I was jotting down descriptive words that came to mind. The BTs caused me to write "mellow, natural, earth tones, clean fundamental and clarity." The SDs elicited "scooped, processed, extreme, aggressive and biting." These descriptions seem to sum up my impressions regarding these pickups. If I were doing lots of slapping or any sort of aggressive playing, I'd choose the SDs. If I were primarily playing more mellow material, I'd go for the BTs. Lastly it's important to note that with selective use of the on board EQ you can make one set of these pickups get within spitting distance, tone wise, of the other. So in the end, you aren't completely boxed in by what pickup option you choose for your Lakland.

Reference Systems
Amplification: Demeter tube preamp/power amp combination driving both a SWR Goliath II 4X10 and an Eden 4X10 XLT.
Recording: SansAmp Bass Driver DI into an ART Levelar tube compressor recorded on a Roland VS-880, using no data compression at 44.1 khz. Monitored using Event 20/20bas near field monitors.