Converting PWM to DC voltage
Will a higher order filter (Sallen-Key, Butterworth, etc.) work better
than just a basic active RC filter?

Yes it will. It'll be better because, as the &quot;order&quot; of the filter increases, the PWM switching artefacts seen on the output get progressively more reduced in amplitude: -

Picture from here.
So, in the above diagram you have a pass band where the frequency response is maximally flat - this covers DC to some cut-off frequency. Above that cut-off frequency you want to attenuate AC components of the signal and ideally, your PWM frequency will be at least ten times the cut-off frequency.
So, with a first order filter you get 20 dB attenuation but, with a 2nd order filter you get 40 dB of attenuation at ten times the cut-off frequency.
For a 3rd order filter you get 60 dB attenuation at the cut-off frequency. In case you didn't know, that's a real-number voltage attenuation of 1000:1.