Twintube will never have the handling characteristics of a monotube. OE's use twintube for a variety of reasons, but the big 2 are cost, and mot cars running twintube shocks are targeting ride frequencies low enough that there's very little chance they will overheat and aerate the damper oil on an all stock vehicle.
Bilsteins are setup as B4 Tourings (stock replacement, twintube), B6 HD (monotube, performance, fine for stock rideheight), B8 Sport (usually same valving as HD's for most applications, but shortened for use with lowering springs).
For a stock rideheight vehicle, you WILL see an improvement in handling with HD's. Can't always guarantee the ride quality will be as good, but it'll be more fun. Plus as others mentioned - lifetime warranty. And Bilstein will also custom valve them for you upon request if they're getting rebuilt, for an additional charge of course, and their guys are top notch at getting EXACTLY what you want.