My current partner and I take turns driving. One shift he will be the driver and the next shift I will be the driver. Currently, he is a basic, but he just started medic school so this time next year we will be a dual medic truck, unless one of us gets moved between now and then.
Regardless of who is the "driver" for the day, if we have an obviously BLS patient, then my partner takes the run. If I have any doubts as to whether the patient could go BLS or ALS, I take it in. (And, since I am a relatively new medic, this happens alot! I probably tend to be a bit overly cautious, but that is better for the patient than me blowing off every other run.) Obviously, as the medic, I also take all of the ALS runs.
We have a good working relationship, and if we are getting slammed with BLS patients, we start rotating those runs so he doesn't get killed with paperwork. Also, if we have a patient that he isn't sure about after I have decided to hand the patient over, he won't hesitate to speak up and have me take it in. Most of those patients, I BLS to the hospital, but there have been a couple times where his gut has been right and they deteriorate enroute and I end up making them ALS. Fortunately, that has only happened once or twice.
Most of the time, my partner does the restocking of the truck. Not because I won't do it, but because along with doing a paper report, once we get back to the firehouse there's computer based reports that we also have to do. If I was the tech on the run, I am busy with that while he is restocking the truck. The exception to that would be if it was some sort of big run, and then I will help to make sure we get everything back on the truck before doing the computer report.
Like everyone else has already mentioned, it totally depends upon the system you are working in and the partner you have as to what the duties of the basic would be on the truck. Just thought I would share how my partner and myself have worked it out.