In my limited experience I have seen bigger vehicles in both GLA and been in one in MEL, I didn't ask for it though. Both chauffeur services were contracted out so it probably depends on that comapnies vehicle stock and useage. Emirates probably don't want to commit as they can't be sure they will be able to deliver. I think you can only cross your fingers and hope for the best!
Re: phone call the day before if you give your mobile surely they will call?