To be fair, the budget reduction didn't hurt the visual aspects of Supergirl in any way. The Budget was reduced by moving production out of Los Angeles/Hollywood proper to Canada (where the other Berlanti shows were already being filmed.) I thionk they also renegotiated the licensing fee to be lower for the CW then what the CBS network (yes, same parent company different divisions though.)
But the ST: D situation is quite different. CBS has pegged it as the 'Flagship show' that they want to use to grow CBSAA subscriptions in the U.S. I think they are even considering talking CBSAA international, which would mean ending the association with Netflix internationally and meaning if CBS decided to continue with ST: D as the 'Flagship show'; they'd have to shoulder the full production cost of any future seasons.
I guess it depends on how 'Gung Ho' CBS is to try and spread their service internationally, because I'd say profit wise (and assuming Netflix remains interested) CBS would make more money in the short term continuing ST: D form at least a second season under a similar arrangement they currently have with Netflix and Space in Canada.