If you compare them by OWAR which takes hitting and position into account, then Greene has the lead 2.8 to 2.1.
So, the big difference is fielding. B-Ref uses the DRS statistic: Rodriguez 12 runs better than average (roughly 1.2 WAR) and Greene -2 runs worse than average. That is a huge difference.
Is Rodriguez really that much better defensively this year? Looking at the statcast numbers, Rodriguez is 9 outs better than average and Greene is average (0).
Fangraphs has Greene with 3.0 overall WAR and Rodriguez 2.4. FanGraphs has used UZR for WAR in the past, but they are not showing any data for 2025. So, I am not sure what they are doing this year - either they are still using UZR and they are just not showing us or they are using a different stat now.