Ubuntu has gotten Sol out of a large economic and social crash following the node collapse. Saying that they wouldn't be up to the task of administrating a large interstellar community ignores several key points about Ubuntu, namely that one of its core principles is to never stop questioning their methods and altering them swiftly and decisively if they turn out to be rubbish.
Very true, but that was several years in the past. The UEF as it stands in the present (i.e. the future

) is governing over a fairly stable, fairly porsperous system. They'd have to adapt significantly to tackle the issues in impoverished human colonies, which are used to years of Terran assembly heavy-handedness and not Ubuntu's softer touch.
Also, you keep saying that the UEF spends less on its military than the GTVA does. Fair enough, it's true, they do do that. There's a parallel here between the EU and the US. America spends billions on its military, while the countries spend a proportionately smaller amount. Now, Americans keep saying that us euro types can only afford to do so because of their spending. Which might be true. However, it may also be wrong. There is no way for us to know for certain.
Again a true point, I'm not saying however that I
know for certainty how such and such would pan out, it's simply an opinion, one I believe to be the most accurate but could easily be wrong.
Your example is a much different scenario though, the US has interests al over the globe to 'defend' and it's military has always traditionally been a political weight as much as a fighting force. We don't have the same amount of support for our militaries as they do, speaking in general of course. I could probably argue that the US could likely achieve it's standing deployments and it's operations with half the force it does now, a lot's to be said for a country having a big military especially when talking to other countries.
The GTVA has a large fleet because it's a part of their deal: we'll keep you safe and we'll do it because we have a lot of ships. Even if the populace knows it's now bullsh*t it's still a lot to know that there's an armada waiting to tackle the Shivans should they ever come knocking again. With the smaller forces an Ubuntu-GTVA would
likely field the effect on the populace wouldn't be there.
Hem. May I please remind dev team members not to take sides too strongly. Players are encouraged to have their own opinions on the war and the strength of the two sides. 
And I do want to note that the Ubuntu socioeconomic models honed in Sol would not translate well to every system of the GTVA. There's significant risk of an administrative 'crash' in scaling up like that.
Ninja'ed. That's the thing though you really can't take any side strongly at all, it's grey on grey after all. I still symapthise for the UEF if only for their much fairer, much kinder Ubuntu than the Terran Assemly's muscle flexing.
EDIT: Spelling Ubuntu like Ubunut is really easy to do.