From a big picture perspective, Atlanta is strategically more important than Phoenix.
If Atlanta relocates (as it seems is the case), the NHL takes a hit in the South and South Florida. The NHL went into the South with a cluster of teams to help raise awareness and exposure to the NHL in the region. To some extent, it is working. USA Hockey reports that youth hockey registrations are growing the fastest in Florida, Georgia, North Carolina and Tennessee (from fairly modest numbers, but a 100% growth in the last 10 years). The latest NBC/Versus TV rights package is a testament to this growth (as well at that in the South West). Unfortunately, with weak ownership (and economic malaise) Atlanta has failed to capture that growth in terms of attendance, TV audience, sponsorship and advertising. Also, while Tampa, Florida and Carolina, have better ownership (finally in the case of TB), their attendance and revenues are among the lowest in the league and none of them are even spending to the salary cap median point. Failure in Atlanta COULD have a ripple effect. I'm also not convinced that Atlanta is a market failure as much as it is an ownership failure, but I doubt that distinction will resonate with sports fans in the region. The message is clear, the NHL is a fringe sport in Georgia.
Phoenix ownership is even worse - the league is the 4th owner of the team in the last 10 years (all of whom have lost money) and they are hoping for a 5th owner to play the white knight. The team has never had a break even season. So what it the difference? The NHL has been in the SW corner of the map for much longer and hockey is much more established, particularly in California and Denver. LA and San Jose are selling out their arenas, and Colorado, Anaheim and Dallas have in recent years. California is now sending NHL players to the draft and is a roller hockey hotbed. Denver has a fairly mature NCAA hockey program and Dallas's problems are the personal bankruptcy of the owner. LA, San Jose, Anaheim, Colorado and Dallas were all there before Phoenix and if the Coyotes were to leave, I don't think it would have much if any effect on any of these teams or on the perception of the NHL in the region (outside of Phoenix).
I think the real reason the league is working so hard to keep the Coyotes in Glendale is because someone local - the City of Glendale, is working really hard to keep the team in place. In Atlanta, while the fans may want the team, the owners sure as hell don't. In Glendale, the owners of the arena, believe the Coyotes are vital to the success of the arena. In Atlanta, the owners of the arena want to jettison the Thrasher for more Lady Gaga dates. That has to piss off the Commissioner.