You can't do the latter anymore. The vehicle has to be a partnership asset and dealt with on the partnership return. Now if the member is a member of a partnership, I'm not all that privy to how it would relate to a SCH C, since SCH C is for a sole proprietorship or single member LLC only. But if the vehicle is used in a SCH C business then the vehicle is claimed/reported on that SCH C for it's use in that SCH C business. Would have nothing to do with the partnership however.
Basically, the use of a personal vehicle would require the member who owns the vehicle to make it a "capital contribution" to the partnership. I don't know how that works if the vehicle is not 100% business use though.
@TaxGuyBill you got some insight on this?
