The strange thing to me is that the new Display Pro seems to give a cooler result with my monitor with the same settings,
No unexpected at all. That is why one needs to tweak all calibration aim points to a desired result (usually a visual match to a print). Also not unexpected is for the same instrument to produce different results when driven by different software (on the same display). In a prefect world, all vendors instruments would produce the same results. They don’t!
To answer the OP, if you can, get the bundled colorimeter (which is the newer EyeOne Display Pro).