Not much. No point in using a 6 kV motor if you have a 525 V grid. If you don't - then an MV motor may make sense. But usually, they need to be quite a bit larger to motivate the more expensive cables and switchgear.
One issue on the side of MV, if you have 6600V available already, but you have to buy a transformer to get 525V (or 575V?), then there will be losses in the transformer to consider for overall throughput efficiency compared to running at 6600V. The cost of those losses, compared to the added capital equipment cost of the 6600V equipment as Skogsgura pointed out, would need to be evaluated.
But from a motor standpoint, kW is kW is kW, no difference in performance.
If you would intend to start the motor D.O.L. [direct-on-line] you could encounter a large starting current, which in turn could produce a very large voltage drop and disturb the other motor already functioning. However, usually 250 hp is still possible.
By the way, since copper is the more valuable than insulation, the medium voltage cable could be cheaper.
