Deterministic query complexity and polynomial degree
According to Table 2 in Aaronson, Ben-David and Kothari, the best separation between degree $\deg f$ and decision tree complexity $D(f)$ is $D(f) = \Omega(\deg f)^2)$, achieved by Göös, Pitassi and Watson, and the best upper bound is $D(f) = O((\deg f)^3)$ (perhaps already from the classic work of Nisan and Szegedy).