I think Econ pretty much nailed it here. Vaccines simply trigger the animals natural defenses, getting it ready to fight should it be necessary. End result is an animal who should be "healthier" or at the very least, resistant to the particular strain of bug that was in the vaccine.
Antibiotics on the other hand are WAY overused. I have no idea how many times I've heard someone say, "oh give em a couple cc's just in case, it can't hurt." Those guys I'd like to beat on for awhile.
Lets take an animal with a low level of infection, a few bugs kicking around, a high percentage of weak ones, a few strong ones. Lets leave the animal alone for awhile, and let its own antibodies work on killing the bugs. If the animal manages to throw the infection, the antibodies are left behind, and you have a stronger animal left standing. If it don't kill ya, it makes ya stronger. Sure, eventually the antibodies die off, but the body rarely ever allows them to return to their former lower levels.
That same animal with a low level of infection now gets a 'couple cc's' for good measure. They haven't injected enough antibiotic to kill all the bugs, probably just the weak ones. And antibiotics are generally not overly selective and will often kill some antibodies as well. Now all we have left are the stronger bugs, along with fewer antibodies. They no longer have any competition from their weaker siblings and can now run rampant within the animal. When the animal comes into contact with another animal and passes the bugs along, all thats getting passed is the stronger strain.
Now, that animal with a low level of infection gets the proper dosage levels. All the weak bugs are killed, likely all the strong ones too. But the body hasn't had to combat anything or at least not much. So its not all that strong either. And what if there were one or two mutations kicking around? The bodies natural defenses can often deal with mutations, however antibiotics often can't. So you leave a couple mutated bugs behind, no antibodies to combat them, and all of a sudden you got a new bug that no antibody can deal with and its spread through your herd. Maybe there isn't quite enough of it in each animal to cause an infection, but its there and eventually through feedlots and slaughter plants, it'll make its way to other herds.
So how about an animal thats got a high level of infection? I don't think you should let em die. I say load em up with antibiotics. I generally use an even higher dose than labelled, but never treat for longer than labelled. Its like antibiotics for people now. Often your first dose is heavier than subsequent doses, simply to get a headstart on eliminating the bugs. We've got so many new viruses/bacteria out there now that not treating would be a loaded gun to the economy. Maybe after a whack of cattle are lost, we'd be left with the much hardier breeds of our ancestors, but it would leave many people financially ruined. I believe if people start using antibiotics properly, we can gradually move back to high natural resistance to infection.
Almost as important is what antibiotics to use? I think you should use targetted, specific antibiotics. I don't like broad spectrum ones like Lyquimycin. While the Lyquimycin is going to work on the main infection, there may be another infection in the background that the dosage level wasn't high enough to get the strong or mutated bugs. So now you're back to the under-dosage scenario.
And as I've been told in other threads, the 'modern reality' is that bigger is better. So many smaller ranches have had to expand their cowherds, but haven't had the ready cash to properly expand their facilities. Intensive livestock operations, when overcrowded, are breeding grounds of infection and mutations. Its mother natures natural defense for overcrowding. Elk breeders complain about CWD ruining their herds. Don't run so many in close to one another, and Mamma Nature isn't going to try and thin the herd down.
Of course, the above ramblings are just my 2 cents and may be based on scientific facts as I've dreamt them up after 3 or 4 Coronas.
Rod