An active bass has a built in pre-amp that runs on a battery, usually 9 or 18 volts. As a result, it sends a hotter signal to your amp. Active pickups generally produce a louder sound with more bite, more sustain and greater dynamic range and control. I don't think there is any advantage to using an active bass for the music you are playing. If anything, passive will sound better. I play classic rock, modern rock, blues, jazz and country with passive basses and never have any problems. I have used active basses in the past but got tired of changing batteries. I also didn't care for the hot signal they produce.
"If you don't want the truth don't ask. Make up your own like everyone else does". (Michael Pare as Eddie Wilson/Joe West in Eddie and The Cruisers II).