Selecting the equipment with the optimal 10 MHz reference
What does it mean to have a "clean" 10 MHz reference in the first place? Low phase noise/jitter or super stable 10 Mhz wrt to temperature/aging etc?


Phase noise is usually not the primary concern, because the usual use of the 10 MHz reference input of an instrument is as reference to a PLL generating some other frequency. And this PLL will tend to dramatically attenuate any jitter at jitter frequencies above a few kHz.

Stability against aging and temperature thus does tend to be the critical parameter.


  If it is the latter case: Why would it matter? Say aging: If my setup is stable in short timespans of measurements (say, hours), why would I care if the reference is 10.00000 Mhz or 10.00001 Mhz?


In your measurement it might not matter.

If you want to reproduce your result a year later, it might matter.

If you have a requirement for a particular frequency accuracy, and it's been more than a few hours or days since your instrument was calibrated, it might matter.


  I assume aging is not an issue since and I do not care the exact value of the 10 MHz. 


If your measurement is not sensitive to small errors in the reference frequency, then the accuracy of the frequency reference might not be critical to you.


  Looking at the "Achievable initial calibration accuracy" of the FSW versus frequency error of the SMW and Aging/temperature for SMF (the only given spec) I would go for the FSW (5e-9)


If you haven't recently sent your instrument for calibration according to the manufacturer's recommendations for achieving this spec, this spec is irrelevant.

All else being equal, I might pic the instrument that was calibrated most recently to use as the reference.

But since you implied that frequency accuracy is not critical to your measurement, the whole question is probably moot.