This is a terrific question. I will defer to some more experienced players, and would like to hear some of their opinions, but I do have a couple of thoughts on this topic:
1. I think it depends on your style of playing. If you build large stacks and try to overwhelm your opponents with pure numbers/power, then AA probably makes more sense because speed is not as important. For example if you use large stacks of medium or heavy tanks and infantry and do primarily melee fighting, then I would not get SPAA. If you do most of your fighting through SP artillary (and SP rocket artillary), however...and you fire at your opponents and then back up and make them chase you...then speed is more important and you will want to invest in SP units.
2. I am sure you know this already, but i think it is good to mention... You would not want to invest in SPAA units unless you are committed to paying extra for other fast units (like motor inf. SP ART, etc.). So if you are going to get SPAA units, then you better get SP rocket ART, SP ART, fast non-armored units (like motor infantry or mech infantry) and fast armored units (like tank destroyers). If you have some slow units, like infantry, heavy tanks or regular (not SP) artillary mixed in with your SPAA in stacks, then that is a waste of money, because the SPAA are not going to be able to use their speed advantage at all.
3. You asked about Axis doctrine. Here are my thoughts on that:
a. Motor Inf. is VERY strong for Axis. SPAA works well with Motor Inf. because they are both fast units. AA does not work well with Motor Inf.
b. You mentioned AA gets a 15% buff for Axis. That is true and really helps a lot, but...don't forget that SPAA research is available 1/2 days faster for SPAA. Having that research available 1/2 days faster makes a big difference, makes the SPAA a very strong unit for Axis and helps close the gap between the value of AA vs. SPAA for Axis.
c. Artillary is available 1/2 days LATER for Axis. That makes Artillary a somewhat weaker unit for Axis. SP ART does not have that same weakness for Axis, so the SP ART unit is fairly strong for Axis compared to the non-SP ART units. If you use artillary, then I would argue it is worthwhile to spend the extra amount to get fast units (SPAA, SP ART and SP Rocket ART), so that you do not have strong SP ART units (instead of weak ART units).
What do other people think?? It would be good to hear opposing thoughts on this topic!