My understanding is that there is no problem taking them together (I have been prescribed both for use together later in the year on my intended Thailand trip).
I believe that PREP can be taken ongoing but DoxyPEP is an antibiotic intended to be taken either after an exposure or at half dose for a max period of 28 days - so in my case I will take DoxyPep daily during my 2-3 weeks trip.
One aspect of DoxyPep that I was advised about and quite relevant to Thailand is that when taking it the user is at a significantly higher risk to get sun burnt and as such hats/shade and sunscreen become more important.