Diameter comparison: larger, bigger, higher, greater?
Solution 1:
Greater is a useful word. I prefer it in the contexts you mention. Other minor tweaks might help too.
The general diameter of veins is greater than that of arteries.
...the diameter is defined as the greatest distance between two opposite parallel lines...
I would avoid 'bigger', which can sound rather childish, and 'higher', which is best used with numbers or with things that possess actual or figurative height: temperatures, tides etc. Diameters have no height.