In general MSCs are applied without having concerns whether it would be within same species or within different species .....This question very depends upon the aim of your study, what you want to show, confirm or proof.
I worked with both strains and found significant differences between their bone marrow-derived plastic-adherent cell populations, so I agree that it depends on what your aim is. I had to use BALB/c because of their Th2 bias and went for syngeneic MSC. Even though the operator (me) and the procedure for MSC isolation were the same, the C57 cells (which I was using in a different project involving a model developed in C57 mice) consistently seemed more "MSC-like" (e.g., ~90% Sca-1+, ~10% CD45+ vs. 20% Sca-1, ~50% CD45+ for BALB/c) after using only plastic adherence for selection. However, the plastic-adherent C57 cells may be very similar to further selected/purified (CD45-) BALB/c cells in terms of relevant surface marker expression. My landmark references for inter-strain differences were:
Phinney DG, Kopen G, Isaacson RL, Prockop DJ. Plastic adherent stromal cells from the bone marrow of commonly used strains of inbred mice: variations in yield, growth, and differentiation. J Cell Biochem 1999; 72(4):570-85
Peister A, Mellad JA, Larson BL, Hall BM, Gibson LF, Prockop DJ. Adult stem cells from bone marrow (MSCs) isolated from different strains of inbred mice vary in surface epitopes, rates of proliferation, and differentiation potential. Blood 2004; 103(5):1662-1668.
Sung JH, Yang HM, Park JB, Choi GS, Joh JW, Kwon CH, Chun JM, Lee SK, Kim SJ. Isolation and characterization of mouse mesenchymal stem cells. Transplant Proc 2008; 40(8):2649-54