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. This is my personal opinion on the matter, but one which is also expressed by other physicists (see for example Modern Quantum Field Theory by Tom Banks).