Front end handling, be it twitchy or stable, etc. is determined by a lot more than wheel size. Head tube angle and fork offset play the more important roles. Combined, head angle, fork offset and wheel size determine a number called "trail."
Trail for most road bikes is in the upper 50 to lower 60 number. You can achieve this number with any sized wheel by adjusting the head angle and/or fork offset...hence why so many well-designed small wheel bikes feel as responsive, steering-wise, as their larger-wheel versions.

Those fixies look sorta funny to me, though. I like my wheels to be in proportion to frame size, wherever possible!