AC vs Heater energy usage ?

Sorry, He is probably right. It is not about the voltage but the current or amps is what matters most and on AC units a compressor will pull high current (or amps) . Im not sure how it would cause a black out unless the whole county was using to much current but he may not have wanted to expain all that. Nor do I. Sounds like you are out of luck. Grampa B

I live in Cali too  . That heater had a spec plate somewhere on it Or look at the watts it uses . If you got a small window unit @120 volts usually they use less than 600 watts I can almost be certain a slave heater uses much more The argument they have is flawed You need to produce numbers AKA wattage or amps usage That small ac will use around 600 or less watts if you don't provide proof of that you won't have a leg to stand on Provide him those numbers and I almost guarantee that space heater uses more power than a 5000 btu 115 volt window AC or it'll be about the same Many small heater pack a punch That punch is usually about 800 or MORE WATTS for that heater If it's a old one Then it's a even bigger power hog . 

I live in Ma, don't need AC except here and there on the hottest or when it is really humid out. But we definitely need our heat for 6 months plus out of the year. Still, with all that said, the AC cost me much much more then heating the place does.  15 amps is 15 amps, whether that is AC or heat, but I think the AC will run more then an electric heater increasing the cost for it to run. You need shade, blocking out the solar heating, you need fans blowing through Ice, you can even make your own heat sink using an auto water pump and 12 volt fans. Junk yard can be your friend.

what matters is the wattage drawn and the wattage the circuit is capable of supporting, not the voltage of the appliance. Many older properties have only 15 amp circuits everywhere ...

It really depends on the usage data. But summer time there usually is a high demand on electricity.   An being you in California wouldn't surprise me if they have extra power charges in summertime. 

Do you pay rent?  If not then the rules are the rules get a fan.  If your in a low humidity area you could use a swamp cooler  to keep cool.  Just Google swamp cooler.  It basically a fan with water.  Sometimes a mist or a wet cloth.

It's not the voltage, it's the wattage that matters.  Find out what the wattage of grandad's heater was and the wattage of the a/c you're interested in and compare the two.

Or resolve the matter simply by using a fan.