Yeah, as much as it pains me to say it, the UNSC would get stomped by the Republic. Especially if were talking post war as you say, when humanity has just been massacred almost to extinction by over 25 years of brutal war.
Now, if we throw in the Covenant alongside the UNSC, things even out a bit. But ultimately Star Wars still wins. Now, I'm by no means a hard core Star Wars fan, but from what I do know about the universe, their hyperspace technology, starship tech, Jedis, the force, etc, puts them a peg above the Covenant. I mean, just looking at Jedis, they're like the Spartans of Star Wars, except during the time of the Republic there were way more of them. I'd say UNSC+Covenant vs. The Republic plays out similar to how UNSC vs Covenant did in the Haloverse: It's a long war of attrition, but eventually, once the UNSC/Covenant gets worn down and The Republic has a chance to fully militarize, Star Wars pulls off the win.
Now, if were talking Star Wars vs Forerunners, then its a complete roflstomp win for the Forerunners. Even without the Halo rings. Even if you give Star Wars the Empire they still get owned. IMO that's probably the only time Halo would win a match up vs the Star Wars Universe. The Republic is a highly advanced galaxy-wide state. The UNSC/Covenant, which are of lower tech and who's control only encompasses the Orion Arm of the Milky Way galaxy, just couldn't stack up.