Besides the built-in preamp the other difference is that active PUs have less turns on their coils compared to usual passive PUs. That makes a way different signal right from the start.
However their frequency chart is typical, it's like a cat's arched back.
To get the lows right treat your passives with an eq where you lower the bass some. Easy.
The get the highs right might be impossible though. The highs of your passives might role off way earlier then the highs of your actives and an eq is not able to amplify highs that don't exist. Also passives cause a resonance peak, which actives don't do or don't do that much (less turns, less peak). Turning down the poties on your guitar lowers that peak, but it steals even more highs. Also an eq could iron it out some, however you need to know exactly where the peak is.