Modern tactics and firearms clearly give the overall edge to modern warriors.
You'd think so, wouldn't you? Certainly the Special forces types are going to have a clear edge in combat, twofold, actually. They will have an advantage because of who they are, and what they know how to do (combat training), and they will have an advantage with the modern arms they bring with them. At least, until their ammo runs out.
And that's something likely to happen fairly rapidly, unless they can break from their training enough to not burn through their limited ammo supply in a single fight, or two...
Also, how are they getting around? Modern fighting men, even the cream of the crop are not, as a group well experienced with horses. Certainly not to the lifetime's experience level that nearly everyone in the "gunfighter era" was.
Sure, they'll learn pretty quick, but the curve will be steep.
Also, just for snits and giggles, why not replace your small group of SF warriors with a squad of 1973 draftees? How do you think they would do?
I think it more likely that they, as others have mentioned, would simply "melt into obscurity", and use their modern knowledge to become wealthy.
one Sci-fi book I read, so long ago I no longer recall the title or author, but do recall the bulk of the plot went like this; Rich oil guy's company accidently discovers time travel. Oil guy recruits mercenaries to go back and prevent the fall of the Alamo (and thus Mexican oil lands will be in rich oil guy's family). The kicker is that the time travel is only one way, for living things (cellular replacement - too much time in the past, come back to the present with parts missing)
The Mercs are not told this, they are told they will be retrieved, and well rewarded. One of the lab techs that accidently got sent back with the mercs tell them the truth. They do defend the Alamo, with M14s and M60s. After the fight, and the Mexican army withdraws, the mercs try to figure out what to do.
(this is the point of my telling the story) - One of them says "I'm going to change my name to Sutter, and go to California!" (Alamo 1836, CA goldstrike 1849...) get the point?
And just FYI, in the book, Santa Ana comes back a couple days after the mercs leave, and takes the Alamo. (he is convinced to return by a staff officer who is a "time cop" sent back from further in our future to correct things).
Net result in modern times, the date on which the Alamo fell is a couple days different in the history books than it was before the time travel. And that's all.
its fun speculation.