I did this test with my double baffle B15N. I was refurbishing the cabinet and the fiberglass on the back wall was in rough shape. I wanted to replace it with a different material that wouldn't itch or have health issues since the fliptop amp was being opened and closed whenever it was moved.
I ran a studio reference disk, some CD's, and played through the cabinet without and with various amounts of lining and listened. The bottom line is that it made a big difference to the mids when the cabinet was lined. The mids lost their muddiness, there was more articulation and delicateness in the notes.
At some point, I couldn't decide how much stuffing was necessary. As I added more, it was difficult to determine if the thicker lining was making a difference. The differences were subtle. Perhaps ear fatigue was setting in.
The problem with this model of fliptop is that there is very little space between the back of the cabinet and the amp head when it is flipped. Too much stuffing and the fliptop can't flip. In the end, I wound up using layers of a dense wool felt covering all surfaces within the cab. I used a second layer on the back wall that arches over the top of the cabinet where the lid sits. This gets removed when I need to flip the amp.