As many will tell you, you can ride an audax on any bike, therefore your current bikes are both 'audax' bikes.
However, I suspect that is not the main purpose of your post. (just call me Sherlock

)
The type of bike often referred to as an 'audax-type' bike, is usually one where :
- the geometry is more 'relaxed' - ie ultimate (race) speed is slightly sacrificed for comfort
- frames are often steel or titanium
- fittings are provided for both mudguards and a rear rack
- wheels are higher spoke count (32 front and 36 rear is common) for robustness - but at the cost of a weight penalty
- it looks best with a Brooks leather saddle

Depending on your style of riding - racing snake/ fast day rider/ steady plodder going on forever - you may well find that either of your current bikes would be fine.
Of course, if you have some £££ burning a hole in your pocket ...
Personally, I have a
Condor Fratello - steel frame (very comfortable), relaxed geometry (good for hilly 300km so far), rack and mudguard fittings, Brooks saddle

.
There are loads of good 'audax-type' bikes out there - having a bike that is well-fitting, comfortable and quick enough is what you need.
Paul Hewitt is a good place to look too.
