Back to the original subject:
I don't plan on rooting the phone, infact I'm probably gonna use it primarily as a small tablet. Which of the 2 versions runs more smoothly for game play, internet surfing, and viewing movies ?
If you are going to use it as a tablet, use either a GPe or GPe ROM on the Sony edition, alternatively something like CM, CandyKat, SlimKat or PAC. The reason is very simple:
Sony ROMs break the notification bar (4.4.x based) when DPI is lowered to 240 and phablet/tablet mode is enabled
They just can't handle this mode at all because of the quick toggles modification Sony implemented. What happens is that the notification area becomes completely empty. Because of this, the only ROM choice for a 240 DPI Ultra is either the GPe ROM or other AOSP/AOKP/CM based ROMs since they handle this perfectly.
I would still go for the Sony edition due to a better ROM selection even if I currently use the GPe ROM on my device. On the other hand: if the idea is to use the GPe and perhaps a custom kernel together with Xposed Framework rather than other ROMs, then the Google edition is an adequate choice.
Still: The Sony ROM is completely out of the question as a phablet/tablet ROM because of this notification issue.