If no plugins or eq etc are in use then DAWs may output very slightly different audio files due to differences in things like how they round up or down when doing their sums or minor differences in how they handle dithering, but the difference is - or should be - so slight it's barely noticable to ears if noticable at all.
The sonic characteristics of modern DAWs mostly come down to plugins, different eq processing algorithms or modelling, dither mathematics and so on, not any noticeable inbuilt differences in the results produced by the audio engines themselves when presented with a simple unprocessed audio track.
Pick a DAW you can afford that runs on your hardware and operating system of choice and has an interface and workflow that suits you. No-one is going to be able to spot from the finished product whether you used Sonar, Pro Tools, Logic, Live, Cubase, S1 or some other DAW. The people who insist you must use Pro Tools "because it's the best sounding which is why the pros use it" are indulging in the same kind of magical thinking that persuades "audiophiles" they need to place a few little wooden discs around the room or swap their amplifier's volume knob for a wooden one to "make the mids smoother and the treble warmer".*
In reality Pro Tools became a near industry-standard because it could handle high track counts and the HD system's hardware and software combinations were created by Avid to ensure they would "pretty much just work" back when computers had a lot less power and were more crash-prone than they are today (no studio wants to run the risk that a computer crash means a great performance never made it to disk).
And once tens of thousands have been invested in a system and the users know it backwards, changing to a different system carries the costs not only of maybe replacing that hardware but the time to learn the new setup and optimise everything.
In the world of commercial studios time very much equals money so the incentive is always to stick with what you have and know and only make changes cautiously and for very good reasons.
*I kid you not. Both these "hi-fi enhancers" exist or at least they did recently. And will set you back several hundreds of dollars, pounds or euros should you believe their creator's claims.