Using an internet browser via gamepad was always a chore, so it's no wonder, that the share of network traffic generated by consoles was always even under 0.2 percent.
Desktop PCs, notebooks, tablets and smartphones will always be more suited for the quick internet access, but at least the constant downward trend of the console share (0.14 to 0.08%) seems to have stopped with the launch of XBO and PS4: http://gs.statcounter.com/#all-comparison-ww-monthly-201208-201312
Especially the Bing integration of the XBO (searches per voice command) seems to be used a lot, Xbox matches Nintendos browsing shares after just a month. Touchscreen browsing via 3DS and WiiU narrowed the gap to Playstation devices over the year: http://gs.statcounter.com/#console-os-ww-weekly-201233-201401
Do you expect the overall console share of network traffic to grow with the new generation or will the internet usage of smartphones/tablets grown even faster, pushing that console share again under 0.1 percent? Will the XBO be the number one when it comes to console browsing or will Nintendo and Sony enhance their browsing integration to compete?