Both charitable giving vehicles allow a wide range of assets to be contributed. Generally, most items that can be appraised and sold for cash are accepted. However, it is important to consider there may be problems with donating more illiquid items to sponsors of smaller-sized organizations. Smaller-sized charitable organizations may not have the infrastructure to go through a lengthy sale process and therefore must limit what items they can accept. Through a private foundation, it is determined by the range and ability of the staff hired. This allows the level of flexibility to be at the foundation's discretion, likely allowing any potential asset for donation.
https://www.fidelitycharitable.org/guidance/philanthropy/private-foundations.html
https://www.fidelitycharitable.org/guidance/philanthropy/what-is-a-donor-advised-fund.html