A lot depends on both the weather and what I am doing.
As a general rule I will take my ECV (which is smaller and much more manueverable than Disney's rentals) into shops and attractions which have long queues.
For restaurants I will either use the stroller parking or someplace closer to the entrance. If the weather is bad I will usually park it inside the restaurant rather than leave it out in the rain.
I think the answer is that it is a judgement call. The CMs are more likely to leave ECVs alone than strollers which they will move.
I don't know about ECVs, but I was instructed by a CM to park my wheelchair with the strollers. CMs will move a wheelchair to the stroller parking if you park it elsewhere (at least they did with me).