Well... no. Not DAW's. A DAW is a "digital audio workstation". It simply facilitates a vast feature set for manipulating and producing audio. All DAW's perform mostly the same functions, and some DAW's have better implementations for certain kinds of functions. Your choice of DAW depends on which of those functions you find valuable.
For example, most of FL's workflow (in the arrangement timeline, automation, track/channel management) is really poorly designed and inconsistent (it basically via interface feedback rewards clutter and you have to spend years learning how to beat it into submission), but it has a great piano roll and a really easy routable mixer. Pro Tools is extremely efficient at editing and processing waveforms, as well as creating recording matrices for I/O, but does not have a good piano roll. Cubase is really good at MIDI editing. Studio One's mixer actually kind of annoys me because there's no polarity switch on the mixer channels. Little and big things.
If you want to write different styles of music, you have to learn how those styles work compositionally. Once you grasp the fundamental concepts of the instrumentation for a style and how it's written, then yes, you can then go out and look for sounds that satisfy those instrumentation requirements. There's lots of stuff out there in the VI market, and you can get really specific with what kind of sound you're looking for (for example aggressive electric bass vs. smooth electric bass, or nylon vs. steel acoustic guitar) and you'll be able to find something.
Then if you were to identify that say "I work with a lot of orchestral VI's and spend most of my time in MIDI automation" you probably would want to pick a DAW that's good at MIDI editing. Or "I record live performance and instruments a lot" you probably want to pick a DAW with decked out recording features, like take selection, layers, easy compositing, etc. Or, say, you want a DAW with good creative features, you'd pick something like Cubase with its chord track.
No one DAW does it all, unfortunately. I primarily favor Studio One right now because it makes most of what I do really fast and painless, however it's still new and lacks big defining features. Track templates like in Sonar, FL's MS Paint style draw tool, Cubase's chord track, a god-damn phase reverse button, etc. If it had all those things I'd be set for life.