Assuming you're looking for a rigorous book and you're at the right level for one, these are probably two of the very best choices.
Either of these will be enough for single-variable calculus, and there is no real reason to read both.
My advice would be that if your main interest is pure math, Spivak is better. However, it should be supplemented with other books covering at least vectors and complex numbers.
If you're mainly interested in physics, have a reason to want to get to multivariable calculus soon, or are otherwise ambivalent about pure math, then Apostol is probably the better choice due to more coverage of applications, curves and non-calculus topics, as well as the second volume. But the second volume is not ideal for pure math because some proofs are left out on line and surface integrals and attention is restricted to dimension <= 3 for this material. (This concerns Chapters 10-12 of Volume 2.)
Overall, my judgment is that the initial level of ability needed to be successful with Apostol is a bit lower, but the difference is small.