Ignoring intervention by Q or similar entities (basically, a Goa'uld vs. Federation/Fed level players fight), the Goa'uld win.
The UFT (and other Trek powers) are advanced enough that the Goa'uld will take them seriously. It won't be the Goa'uld playing games, messing around with slaves, or deploying Jaffa armies to conquer. Goa'uld will jump hosts into captured Trek personnel to gain knowledge; instantly gaining a complete Trek technical education, political information, societal information, etc.
More importantly in many respects, the Goa'ulds initial plan will be genocide and planetary destruction. The goa'uld both have and use, as a standard weapons system against non-Goa'uld enemies, bio weapons that will depopulate worlds and bombs that will glass planets.
The goa'uld opening move (at least once they captured a single individual and gained the relevant information) would be an entire fleet of Ha'Taks appearing out of hyperspace in Earth orbit and wiping the entire planet in about five seconds, before proceeding to go down the list of federation worlds doing the same thing.
And if the Goa'uld are seriously pushed? Then they do what they did in the golden age of the goa'uld (when they were conquering the Milky Way in the first place) and start mass implantation. All of those symbiotes are pulled out of the Jaffa and implanted en masse into the human slave population. Everyone of those humans instantly becomes a superhuman physical specimen (not quite augment level, but fairly close) who is a master of basically every skill you can think of.
Trek use of tech-of-the-day / superweapons / godly intervention would give them the win, but absent that the goa'uld would win simply because the Trek powers are all utterly unprepared for how the goa'uld view war and how they act.
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People make the mistake with the goa'uld of viewing them through the lens of the SGC while ignoring the actual realities of that conflict. Nirrti implanted nano-tech in Cassandra that would self assemble into a bomb that would trigger the explosion of the Stargate and in the process wipe out a good chunk of North America. Apophis implanted Ryac with a planet killing bioweapon. Anubis threw an extinction level asteroid at Earth, one boody trapped to nova the Sol system if Earth reacted as expected. Ba'al once blew up a planet just because he was a sore loser and didn't want it to go to another goa'uld.
When Earth became a minor annoyance to the Goa'uld, they were prepared (as a collective) to send a few hundred Ha'taks to sterilize the planet. The only thing that prevented that was the Asgard buying them off.
And up until the Replicators decided to genocide the Goa'uld? They were sill the galaxies dominate power.
Anubis lost two of his super mother ships and the goa'uld as a whole lost Ha'Taks by the hundreds in their succession war over the ~10 years of the show between Ra's death and the Replicators wiping out the goa'uld. And despite those losses, the goa'uld were still going strong, still the unquestioned dominate power in the galaxy, and still saw Earth as basically a minor annoyance to be crushed whenever it became convenient/useful.
The Jaffa were never the base of Goa'uld power. They were bully boys who kept the human slaves in line, incubators for future goa'uld, and the pieces used in the Goa'ulds real life RTS game that they played to stave off boredom.