Is there a way to measure the overall feel of the weather for a place?
Suppose that:
Place A has Temperature $33^o C$, Humidity $57\%$, Wind $14\;km/hr$, and Precipitation $20\%$
Place B has Temperature $37^o C$, Humidity $11\%$, Wind $14\;km/hr$, and Precipitation $0\%$
Which place would feel better?
One measure that could be used is the apparent temperature, which combines air temperature, humidity and wind speed to derive the temperature that the human body feels. It is sometimes referred to as the "feels like" temperature or the Steadman temperature, after Robert Steadman who proposed the idea in 1971.
The formula used by the National Oceanic and Atmospheric Agency, for calculating the apparent temperature is:
AT = -2.7 + 1.04*T + 2.0*e -0.65*v
where AT and T (air temperature) are °C, e is vapor pressure in kPa, and v is 10m wind speed in m/sec.
Most weather oraganizations include the calculated apparent temperature in their weather reports.
Indeed, there are some standard measures of apparent temperature which are derived from important things like body heat loss, as well as all sorts of proprietary formulations such as Feels-Like temperature that attempt to throw in many extra factors.
But in the end, different people do indeed enjoy the feel of different climates, and so it becomes somewhat subjective. Not sure a large percentage of the population agrees, but I actually much favor the the feel of moist hot weather as opposed to dry hot weather with the same temperature. And I've known others who will get shivers anytime the temperature drops below 80 °F (26.7 °C). So when you say "feel better", indeed any estimate is going to be debatable in its validity.
Also note, it'd seem hard to incorporate the probability of precipitation into a comfort metric in a meaningful way. It either rains or it doesn't; a 20% POP day feels the exact same as a 0% POP day, all other conditions being equal, if the rain doesn't occur. Now obviously getting soaked may not be the cup of tea for everyone... but there are some!
