Forgive me if a wax on a little bit on this one, but . . .
I love old math books; and I think, provided one takes the requisite care to "translate" what is sometimes older language, they are a great source of knowledge. And I think that sometimes being closer in time to "the source" lends a certain clarity of vision. There's nothing like reading ideas from the guy who first had them, or from his immediate students.
As far as rigor is concerned, well, some books have it and some books don't, and that has little to do with age. If you can discern a rigorous argument you will recognize one when you see it, no matter how long ago it was committed to paper. Think Euclid, think Archimedes.
A few of my favorites: Poincare's New Methods (not sure of the date); Von Neumann's Mathematical Foundations of Quantum Mechanics (1932); Artin's little book Galois Theory (in the nineteen forties, as I recall); Courant and Hilbert's Methods of Mathematical Physics (German edition, 1937); another oldie but goodie is Paul Garabedian's Partial Differential Equations (ca. 1965?), old but very clear and rigorous (a grad student of L. Craig Evans (yes, the Evans) told me it was outdated); all are "antiquated" by the standards of 2015, but what great sources!
Not to leave physics out altogether, will Feynman's Lectures ever be outdated? How about Dirac's Principles of Quantum Mechanics? True, these books adhere to a physicist's standard of rigor, but there is a lot of math to be understood from both of these guys; so do I opine.
An anecdote to close: when I was a kid learning calculus, I struggled and struggled with Thomas, a de facto standard in the 1960s. Then my old maid aunt--she was a math teacher on a Navajo reservation--gave me her copy of Lynman Kells' Calculus (1949). The scales then fell from my eyes . . .