A team will have no problem attracting high-profile UFAs for the most part as long as they are viewed as a contender, or perhaps a step before being a contender. Players will take a bit less to be part of that, or take equal money but prefer a destination that includes being a solid contender.
Under Sutter, it didn't change at first while the Flames didn't do anything special. Drury couldn't wait to get the heck out of here, for instance. Sutter quickly realized this as a GM, and made an emphasis on drafting WHL prospects (as well as a general lack of physical scouts to cover enough leagues anyway) as it would give the Flames a slight advantage in 'being closer to home' in the first place.
Once the Flames made their '04 run, I do think that more players were willing to sign here. Even with the first couple of disappointments, I think more players were willing to sign here than not. However, after missing the playoffs for a few seasons in a row, Feaster couldn't throw enough money at free agents like Brad Richards to convince them to come.
I think players will always go where the money (including tax implications) is first and foremost, then it is a chance to win, then it is the expected role, then stuff like team mate familiarity, climate, preference for playing in a hockey market or not, etc. Money first, then the chance to win, then everything else IMO. Players will take a bit of a haircut to get a real chance at competing for a cup, but not much it seems (at least usually).
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