Switching to Active from passive?

Just get better passive pickups.

I've got some great Seymour Duncans on my Lull. Fralins are supposed to be good.

 

I wouldn't say it's pointless running active pickups without onboard EQ. Active pickups are are more than just pickups which need a battery; they're less susceptible to noise and, due to the preamp, require less winds and weaker magnets which means less string pull. You can run active pickups with just a standard vol-tone setup and still derive the benefits of the technology.

Another thing worth considering is that, unlike passive pickups, you won't need to run an earth to the bridge, meaning you're not using your body as a ground and, therefore, far less likely to be electrocuted

 

As Doctor J says, you can run actives with passive controls. Most people ran EMGs this way for years until onboard preamps gained wider popularity. If you decide to do this, most control cavities have enough room to tuck the battery underneath the pots. Just make sure you put something between the metal battery and the pots so you don't short anything out.

Another active J pickup set that doesn't get as much attention is Schaller. I've had a set in a J bass for many years and they sound really nice. I've always preferred them to EMGs, personally.

 

I had a set in a Squire jazz a few years ago. The battery squeezed into the control cavity (very very tight squeeze btw) and they worked fine. Aero and Nordstrand are also 2 pups to consider.

 

If it were my bass I'd forget about active pu's and install an inboard EQ first, you can go from active to passive on the fly by adding a mini switch.
If you're still into replacing just the pu's, a decent passive set like the Dimarzios you mentioned or Bart's or SD's and a series/parallel mini switch will liven up your sound.

 

I bought my first Active 5 in 1991 and never went back.
Time & time again bands were saying that my bass really stuck out well in the mix.
Give it a try, you can always go back.