I'm probably biased towards the risk posed by big ships because I spend most of my life on the things
Seriously though, if you're talking about close quarters incidents, the risk with a big ship is, simply, size.
At night, or in poor vis, a large container vessel /VLCC can block out the horizon from a small boat to the point it is almost invisible. If you're doing 20 knots towards a yacht, and suddenly realise it's there, almost any change of course will get you out of danger, either a U turn, or around the bow / stern. If you're faced with something 400m long, and suddenly realise it's there, then the around the bow/stern options suddenly disappear, and the bow wave will probably make the U turn option pretty difficult.
And it does happen - I had a rib stuff itself into the middle of our vessel a while back, claiming he had seen the superstructure and thought it was at the stern (we are a large salvage tug and the accommodation is all forward). He therefore attempted to skirt around the stern - only to find he was midships
The only funny side was that he hit us almost in the middle of the large yellow painted letters saying "Rescue Zone"