Problem is abandoning your car while sat in a live lane is a dangerous activity, no matter which door you choose. Indeed, there is some argument for using your eyes and abandoning ship via the drivers door on a smart motorway, and thus getting to safety 5 to 10 seconds quicker than you would if you fannied about scrambling across the interior. On a hard shoulder you'll likely have the benefit of time to pith about climbing across, time you simply do not have when stationary on a live carriageway if you value your life.
And of you're my size you've zero chance of being able to climb across anyway...