Well, I've got nothing else to do, so I might as well flesh this out. The OP, of course, is no help: the parameters of the war/battle are not even defined.
On the one hand, the OP uses the term "battle" to describe the conflict.
Merriam-Webster's third definition for battle[1] is "a general encounter between armies, ships of war, or aircraft", viz. a tactical engagement.
However, the phrasing of the language around the Twelve Colonies and the UNSC in the OP implies to me that this is, in fact a long term engagement between two large organizations, thus, a war.
In this post I will assume that the OP refers to a war, rather than a battle.
The initial military assets of the Twelve Colonies are stated by the OP: 120 battlestars, "thousands of Vipers" and "all of its infrastructure." Unfortunately, we have little understanding of the support infrastructure or proper escort fleet that goes with a battlestar, so I will presume the statement implies the battlestars are at maximum readiness (an assumption I was going to make for both sides anyway.)
Note on armament: Galactica-class battlestars have at least twelve missile tubes[2], each of which contains one warhead with, at most, a 150 kiloton yield[3], or roughly a 630 terajoule yield per warhead[4]
The maximum possible initial economic assets of the Twelve Colonies would be twelve approximately Earth-like worlds and other space-based resources (asteroid belts and their mining operations, space stations and shipyards, etc). This is overly generous, but as we will soon see, it makes little difference.
The initial military assets of the UNSC Navy is not stated by the OP, and I am unable to find any numbers that even estimate the size of the fleet. A list of identified ships[5] indicates the UNSC has at
minimum:
6 Carriers (note: the armaments of this ship class are poorly defined)
6 Cruisers (note: the armaments of this ship class are poorly defined)
15 Destroyers
20 Frigates
(note, these ships existed at some point during the Human-Covenant war, and that these ships existed prior to this war is conjecture.)
The initial economic assets of the UNSC are, roughly, "more then 800 worlds [...] at various stages of development." [6]
I would hypothesize, that in a long war, the UNSC completely outproduces the Twelve Colonies and squashes them. In the short term, things get much less easy to predict.
[1]
http://www.merriam-webster.com/dictionary/battle
[2]
http://en.battlestarwiki.org/wiki/Missile_tube
[3]
http://en.battlestarwiki.org/wiki/Galac ... r_Warheads
[4]
http://en.wikipedia.org/wiki/Ton#Ton_of_TNT
[5]
http://halo.wikia.com/wiki/UNSC_Navy#Id ... d_Stations
[6]
http://halo.wikia.com/wiki/United_Natio ... lonization