If you just handed out phage freely, as you do abx, bacteria will "eventually" evolve resistance to phage....at a 2-3 orders slower rate, but it will eventually happen.
Of course, the solution is easy, you don't develop a phage therapy like you would an antibiotic, but rather like a constantly updating flu vaccine.
This was how phage therapy was originally developed, and it's still being done that in some surprising places like Georgia [1]. They have phage 'banks' for common bacterial species, and it's not effective, they end up taking bacterial samples from each patient and isolating more phages.
[1] https://www.phagetherapycenter.com/pii/PatientServlet?comman...
Same with HIV, a high mutation rate complicates making a vaccine.
I was really struck by this part of The Great Influenza:
https://books.google.com/books?id=BYsW6qTP0pMC&lpg=PP1&pg=PA...
Influenza is an RNA virus. So is HIV and the coronavirus. And of all RNA viruses, influenza and HIV are among those that mutate the fastest. The influenza virus mutates so fast that 99 percent of the 100,000 to 1 million new viruses that burst out of a cell in the reproduction process are too defective to infect another cell and reproduce again. But that still leaves between 1,000 and 10,000 viruses that can infect another cell.
More importantly - is mutation rate what we want to consider? Bacteria exchange DNA with each other through horizontal gene transfer and Wikipedia quotes that as the main means of transmitting antibacterial resistance, for example [2], even across species (to the extent that bacterial species are even well-defined). I'm not sure how to make the comparison with that to viral mutation rates. This [3] source gives the following interesting, but imprecise, quote:
> This antagonistic coevolution results from the constant emergence of countermeasures by which bacteria resist phages, while phages, mutating at a more rapid rate than their prey, find means to overcome this resistance.
The paper it cites [4], definitely shows phage evolution alongside bacteria evolving counter-measures. So I think that's enough to answer the original question posed, though the question of "which is evolving faster" is harder to answer and probably isn't very well-posed.
That all said, I know nothing about this field and would be happy for some better insight.
[1] http://www.nature.com/nrmicro/journal/v11/n5/box/nrmicro3003... [2] https://en.wikipedia.org/wiki/Horizontal_gene_transfer [3] http://cid.oxfordjournals.org/content/48/8/1096.full [4] http://rspb.royalsocietypublishing.org/content/royprsb/269/1...
I think it is quite important when considering this particular interaction. Horizontal gene transfer will help a population of bacteria share a successful strategy, rampant mutation will help the virus try more strategies.
The article mentions that the particular infection reached a balance with the phage overnight, so it is likely to be a quite an issue. But the population of bacteria resistant to the phage had become susceptible to an antibiotic (for reasons related to the resistance). So it can still be a valuable tool, even if resistance happens quickly.
That's interesting. Previously I've read that evolution was one of the benefits of phage therapy because phages could evolve alongside the bacteria.