There's one more component to the electrical equation that really matters: watts
Watts= Volts*Amps.
You're right, amps are what can kill you, and it doesn't take much. IIRC, it's like 15 milliamps (.015 amps) across your heart to stop it. Amperage flow also generally dictates the wire gauge needed.
When shopping for a battery, more amps is generally better, indicating the maximum current that the battery can deliver at a given time.
However, a battery is not at 14v while cranking, or even 12. It's more like 10.
220ca*10v= 2200 watts
180ca*14v= 2520 watts
A beefy microwave takes 1500w, so your vmax needs a hefty jolt to crank over. It's why high-draw electrical fixtures often use 220v instead....otherwise wire gauges would be impracticably large to run them on 110. A motor that takes 10 amps on 220 would need 20 on 110 to do the same work.
So "in theory", a 180amp source at 14v would provide more energy than a 220 amp source at 10v. But your battery is only at 14v with the engine running. Shut it off and wait a couple hours, and it will be back down to 12.6 (lead acid produces 2.1v per cell).
That said, a higher amp battery won't lose as much voltage as a lower amp battery when placed under the same load, so wattage output will be higher from both aspects.