Not really, Audax has been going far longer than Sportive's. I've only done one Sportive, about 4 years ago before I started to Audax, and that was dominated by local club riders.
Being unsuported, with Audax you have to be self sufficent, have some knowlage of where you are, and where you are going, and be able to fix your bike if it breaks, with a Sportive, you can just wait for the support wagon. Also they seem to be far bigger than Audax's, numbers wise.
For Audax's I've noticed some filling up early this year, but there are (seem to be) a lot less than last year and more spread out due to no need for the PBP qualifing events.
Audax does have the advantage of being about a quarter of the cost of a Sportive, so you can do a lot more on a similar budget.