Safety of fixed wheels

Hi, no doubt this will cause some controversy but anyways...I used to ride hybrid with 26" wheels for many years but I recently switched to a fixed wheel at the start of the year. However, after a couple of months I took a corner too quickly and wiped out - landing on my thigh and breaking it. Looking back, I can't help but feel that it wouldn't have happened had I been riding my 26" wheeler. Now that I'm recuperating, I'm fearful about getting back on the fixed wheeler. Whatever anyone says, they're X% less stable than a bike with smaller wheels and thicker tyres.

Neg repped.