In general reading entire textbooks in QFT is not the best way to learn QFT (or any subject in science and mathematics).  I have not heard of the books, but my guess is that they are not going to be as rigorous as math books and papers as there is not a mathematically rigorous formulation of QFT (I'm sure you are aware that the basic problem of Yang-Mills existence and the mass gap is a Clay Institute Millennium Problem).

Also to be honest it has been a while since anyone has done anything in algebraic or axiomatic QFT which the wider community of field theorists really cares about.