I'm a little confused about what you have where... do you mean that you're reading the humidity at 80% on the cool side and 70% on the warm side?
Anyway, you want to know the humidity that accounts for most of the air in the tank. You might measure lower humidity on the hot side because the air can hold more moisture the warmer it is; so for the same amount of moisture, the relative humidity (which is the % of how much the air can hold before it condenses, at that temperature) will be lower. But that should only be true for the very immediate vicinity of the basking spot. The rest of the air in the enclosure should be at a fairly constant ambient temp; and anyway, a difference of 10° really won't make much difference in the % humidity.

So just go by what your Acurite says and ignore the analog gauge, which is probably wildly inaccurate anyway. Either way, you do not need 80% relative humidity for a BP.