I question the usefulness of the F11S radio with nighttime shortwave coverage lacking the 31-meter band. Between these two, I would definitely opt for the F12S. But overall, the product doesn't seem to have a purpose for me.
Initially I expressed confusion via Twitter that an eBay auction for an F11S listed the SW coverage as 2.3-7.35 MHz, whereas the product photo showed a shortwave band labeled 6-18. @swlistener replied with a link to an ICF-F11S/ICF-F12S manual that shows the specs for both radios. I was unaware that the F12S existed.
EDIT: XQYZ on reddit pointed out that these radios require two D batteries. After learning that, I wanted to share the dimensions as well. Sony Asia provides dimensions of 216 x 129.8 x 68.6 mm for these radios (8.5 x 5.1 x 2.7 inches). So, these are large portables requiring large batteries, with small shortwave coverage.