The difference is down to the level of inflation volatilty ...

Nice chart .... I'd actually reframe it ... sub 4% yield correlation is almost always positive ... and its almost  always negative above 6% .... between the two its not clear ... which suggests that market context (narrative) intrudes alot ...  you will also note that once you get beyond a 6% bond yields the additional correlation benefit drops away ... because inflation is getting along way out of whack bond yields loose their real yield ... and in practice equities also loose their ability to hedge CPI because margins become unstable ... this is where CRE tends to find a very strong bid ...  particularly if you have indexing leases ...