Tetradure is a brand name for oxytetracyclene. There are many different brand names, concentrations and variations of the base compound tetracyclene. It is a broad spectrum bacteriostatic, meaning that the way in which it attacks a cell is to block the cell from reproducing. It is effective against a large variety of both gram positive and gram negative bacterias.
Draxxin is the brand name for the drug Tulathromycin. It is a macrolide, meaning it is also bacteriostatic. It is most effective against gram positive bacteria.
The biggest difference is that Draxxin is not able to penetrate both the lungs and the GI tract, so it is a great respiratory med. Oxytet. is a great respiratory and intestinal med.
It is not recommended use a bacteriostatic drug with a bacteriocidal drug, like Penicillin, that works by causing the cell to basically explode itself. So, a bacteriostatic drug basically blocks the process that the bacteriocidal needs in order to be effective. This is why I am always reminding people to check for meds that contrindicate, so that when you do treat, you aren't also unknowingly preventing treatment at the same time.
I am not a vet, nor am I a pharmicist. I found all of this information online in either the Merck Manual or by doing searches on the different drug names and simply compiling the research.