There may be differences in yield strength of Ti alloys in tension and compression. It is associated with the forces acting on the grains in the material. The deformation of grains in tension and compression in some alloys are differ. But in the case of differences the more reliable the results are in tension, so use the results from static tensile tests.
Dear colleague, really, these differences are caused by granular structures of Ti alloys and slip of grains. For the reliability of data: better test is that corresponds to stress-stran state under consideration.