Another very important factor to consider is the overall political strength of either organization at the time of the supernova. Because while the franchise hasn't explicitly said as such yet (so yes, there is a degree of speculation here), I am growing increasingly certain that the Romulan Star Empire was already in a political decline by the time news of the imminent supernova broke, and had already declined enough that it no longer had the power and unity to keep things together during the turmoil that followed and eventually crumbled. This is probably why the Romulans sought the assistance of the Federation in the evacuation rather than conduct it entirely themselves, something that normally shouldn't have been such a big problem for them as they should've had the ships and resources already...so it's telling that they instead didn't seem to.
(Not that evacuating Romulus, any other populated/colonized worlds in the Romulus star system, and possibly any other colonies within a couple of lightyears of Romulus--because the deadly radiation of a supernova CAN still bleed, with enough time, into neighboring star systems if a big enough an explosion, which this supernova was implied to be--was any small feat...but that's for another post)
And it wouldn't be that untoward to consider the Romulans politically vulnerable by the 2380s. We know there was a growing Reunification movement beginning within the empire that largely ran against the usual political agendas of the empire at the time, creating division. We also know there was a growing discontent with how the empire was being ran by its general public, further fanning the flames. And we know there was active tension between the Remans and the Romulans as well, which likely spiked after Shinzon's coup. And of course, there was the whole Shinzon incident itself, having taken place just a few years before, an incident which had resulted in the overthrowing and death of both the Romulan praetor (and later, the usurper who became praetor in his stead) and nearly all of the then-ruling senate, resulting in a major disruption in the empire's primary system of government. That's not something you can just rebuild and recover overnight, the ramifications of that were probably felt for years later (and Nemesis ended implying exactly that), enough that they were still ongoing by the time of the supernova. In short, things were not exactly hunky-dory in the Romulan Empire at the time of the supernova, and the supernova was probably the final nail needed so to shatter the already weakened empire entirely.
Meanwhile, though, you had the Federation, which, by all accounts, seemed to be doing pretty well by comparison. The only major problems we've been made aware of by the time of the supernova was a budding problem of it stumbling over its own bureaucracy but not so badly it couldn't still overcome it, and the Synth attack on Mars, an event that may not have taken place, or at least played out in the same fashion, in a scenario where the Federation is the one facing the supernova. Ultimately, things are still going pretty good for the Federation of the 2380s, so I think they'd not only fully survive the destruction of Earth, they'd probably handle it much better than the Romulans had.
Plus, the reason the Federation pulled out of assisting the Romulans in their supernova was mostly because the Federation felt it didn't have enough political motive to (again, whether or not they were right about that choice is for another time). But naturally, if they were to face the supernova instead, the Federation would've had far more political motivation to act and respond accordingly, so much so I have no doubts at all that they would've successfully evacuated Earth and surrounding worlds almost entirely by the time the supernova finally struck, not gotten caught so off-guard by it like the Romulans had and loose millions to billions in the process.
Finally, the Federation has not only several powerful member worlds within itself that could've lent aid, they also have several allies beyond their borders that could jump in to assist in the evacuation, some of which are pretty politically powerful themselves. Heck, I could see even the Klingons jumping in to provide at least some aid to the Federation, considering they seemed to still be on fairly good terms following the Dominion War. Point is, the Federation would've had plenty of already-established friends that could've come help them in their time of need. Meanwhile, the Romulans, ever the isolationists, can't really claim to have much of any allies outside their borders at all, and in fact had spent most of their history deliberately building a negative rapport with the other neighboring powers, which kinda nipped them in the butt when it was in part the lingering tensions with those other powers that caused them to not be there when they needed them most.
So...very long post short (sorry, I kinda got on a tangent there)...no, I don't think the Federation would've collapsed if it had faced the supernova instead. It would've been rattled and weakened, yes, but it would've ultimately prevailed. At the very least, the situation definitely wouldn't have played out anywhere close to similarly.
