There is a third possibility. Speakers, as a rule, distort more the louder they play. In some cases, this is quite noticeable, though not in all cases.
Some years ago, I had a pair of Optimus T-200 speakers, and bought some Heybrook HB-2 speakers (the version made in the early-mid 1980's). At low volumes, they sounded similar, but as I turned up the volume, the Optimus speakers seemed to gradually add more and more distortion. So at reasonably loud levels, the Heybrook speakers sounded much better. But at a little higher volume, the Heybrook woofers "bottomed out" (i.e., were overdriven), and then the Optimus T-200 sounded better at that level. The point of the story, in this case, is that higher levels of distortion at higher volumes is sometimes a natural part of the sound that the speaker makes, and does not necessarily mean that it is being overdriven.
But among your two choices, judging from the specifications for each, it is more likely that the speaker is being overdriven than that the amplifier is clipping.