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 some other theoretical physicists (see for example *Modern Quantum Field Theory* by Tom Banks).  

Edit: If I remember rightly, you can find Steven Weinberg's lecture where he reflects on the fiftieth anniversary of his classic paper 'A Model of Leptons' and at the end he expresses similar sentiments about a mathematically rigorous formulation of QFT (ie. that it is important and desirable, but that he does not particularly care as such a formulation is unlikely to inspire any actual new physics).