It's not so much a matter of small, medium or large gates, it's the radius that defines what can fit where. Often the spots are not even coded as Gates at all so that the default airport vehicles don't automatically show up.
To make matters worse, AI traffic programs namely MyTraffic commonly doesn't use real world figures in the wing_span settings so that even when airport parking spots ARE configured correctly the AI will park in spots that aren't meant for those types.