I haven't seen Spivak but I own Apostol. Reading volume I. It is very thorough. And there is no order set in stone to introduce differentiation and integration. I liked it with integration first. Apostol is also very clear. No BS in his book. Everything comes with a proof and detailed analysis. I strongly reccomend Apostol.
EDIT: The best person to judge this in my opinion is Mathwonk.