Hi,
my own machine (pictured above) has travels of 350mm x 350mm x 350mm (13.7" x 13.7" x 13.7") and is very similar to your design.

I have 32mm C5 ballscrews which are great, very stiff. It did pretty much dictate 750W servos to accommodate the ballscrew momentum though.
25mm ballscrews would have been perfect, still adequately stiff and yet could have used 400W servos.
Personally I think 20mm ballscrews would be underdone.

My machine axes are cast iron and when they start 'rocking and rolling' I rather think 20mm ballscrews would be too compliant (flexy). That is of course only my opinion.

Craig