In this seasoned (old) pluckers opinion, regardless of brand, all (most)round wounds get that bright brillant sound and flats,well are flats and get a bassier ballsier sound and nothing wrong with that! Right. It is after all, Bass!
You will have to experiment with what brands/type work for your individual taste and playing style since rounds generally are a bit rougher texture and flats have a smooth finish. And then theres the life exspectency of the chossen one. I as I believe we all have gotten a dead string right out of the box at one time or another so you do have to keep an open ear . That another story!
I actually prefer Earnie Ball Round Wound extra lights (ok go ahead and laugh! They work for me!)on my Rouge 5 but GHS,DRs and others are fine.
It also come down to gauge and playing style (fingers and thumbs or pick)and technique.
Trying to get anothers identical or near close sound? That's a tough one! Sometimes even for the original player! But the previous comment of using the same type strings (and not necessarily brand)may be the best you can hope for other than equalization,pressence,overdrive etc....
And then of cousre now a days effects can compensate a heck of a lot for sound,style,technique and dare I say....talent!
I've found that I have my own unique sound that always seems to find me which I am content with but when needed I usually am able to get close to another sound by simple equlization adustments and yes... I admit...EFFECTS!