I have two Squier basses that are active. The jazz Deluxe and the Jaguar, and I have to say, the pre- amps in both of them are amazing! Hot, clear and punchy. I don't think the deluxe is still available but the Jag goes for around 300 bucks. In many cases, that's the cost of JUST a pre-amp! I don't know what they do to make them so affordable but I like what they're doing. Kudos to Fender and/or Indonesia, or whoever is responsible.
The Jaguar just has a circuit to boost, add bass frequencies. It still has a passive tone. The Dimension is truly active with being able to add or subtract frequencies.
I know it has a bass boost but the pre-amp doesn't effect the pups otherwise? Because the bass is very hot. At any rate, the bass boost allows for the use of the rear pup and still get a ton of low end.