A compromise you really don't need to make. What freq range(s) are you primarily interested in? Do you often go to a parking garage or other low-ceiling structures? We've got LOTS of links in our Scanner Antennas wiki article (note: all links are in blue)
An amp in a mobile enviornment is likely as not to amplify every and all signals and noise together - a particular problem if you are in an urban environment. Better to improve your antenna than have the potential for overloading, spurs and other garbage. 73 Mike
Another thing to consider is that, with respect to other fixed base antennas, a mobile is low in height - so unless you are up on a hill or mountain, your reception is compromised right from the start, regardless of the antenna you get.
The best solution is to get the best mobile antenna you can get, and get it as high on the vehicle as possible. 73 Mike