Difference between XMSS and MSS-SPR
As the paper of MSS-SPR does not contain any One Time Signature scheme


Actually, that's not true; they assume Lamport signatures (specifically, a version they call LD-OTS).

When using the LD–OTS, the one-time signature of the message consists of
n bit strings of length n. The veriﬁcation key also consists of n bit
strings of length n, since half of the veriﬁcation key can be computed
from the signature.


Hence, the OTS signature is $2n^2$ bits long; in contrast, a WOTS+ signature (which XMSS uses) is $(n/4+3)n$ bits long, considerably shorter.

Now, the difference is actually larger than a factor of 4 - I believe that, if we take account of the fixed overhead of the authentication path (which is the same in both cases), and MSS-SPR's use of a somewhat smaller $n$, the two are closer.


  a fair comparison should use the same OTS in both schemes.


True; however as specified, the comparison isn't fair.

As for why MSS-SPR uses LD-OTS (rather than some Winternitz-based scheme), I'm not one of the designers, and so I can't be certain.  My best guess is that they couldn't come up with a shorter scheme that preserves the "not relying on collision resistance" property (which WOTS+ does).