I do both check the reviews then just watch it, but if I am lazy I can just watch it.
I find Cw shows fine but only if you binge it in one go, I often binge all 5 shows in one go and had no real issue with batwoman in the cross over series with the monitor.
With Arrow coming to an end I think batwoman is perhaps gearing up for a different take on it but it won't suprise me if everyone is like this ain't batman.
Arrow had the same issue in being a poor mans batman so they simply wrote the batman and superman and girl out of their universe due to the tv rights.
Its a long standing problem and rumour is the Monitor and Green arrow are going to merge all universes together and fix the issue so superman, girl, batman and the rest of the dc charactors are at least under the same house.