Like Timmy said, neither. If the speakers are 8 Ohms each and are wired in parallel then the amp is seeing a 4 Ohm load and each speaker is potentially getting 1/2 of the 4 Ohm bridge rated power of the amp, which is likely somewhere between 500W and 1,000W per speaker.
Yes, if the amp is rated at 1000W under a 4ohm load, and you're running two 8ohm cabs in parallel, the amp will see a 4ohm load, and each cab will see 500W of power.
In this configuration, you'll want to make sure that each speaker cab is rated for at least 500W RMS power. Don't confuse this with Peak power handling. The peak power rating indicates how much instantaneous power the speaker can handle for a split second. The RMS power rating indicates how much average power the speaker can handle over an extended period of time (this is based on the thermal dissipation of the cab/coils and physical/mechanical constraints, etc). If you exceed this, you'll likely end up burning your coils eventually. This is obviously bad. The power rating on the amp is essentially how much power it can put out for an indefinite amount of time, so if you have your amps setup powering your speakers at more than their RMS handling, you're just slow-cooking them, and they'll eventually die (assuming you're running signal through them).
So make sure your speakers are rated for at least 500W RMS.
That is not really accurate for several reasons. The simple one is that it ignores the application. In an ideal world one would like to see the power (actually voltage and current) that is appropriate for the application. The 1.5 to 2 times the continuous rating comes from an EAW white paper that has actually been updated to clarify that it is for a generic situation but in an installed system with a known application, it is much better to work back from the desired results to determine the power required rather than assuming the power based on the speaker rating. An extreme example but if 1W provided all the power you would ever need for the application, would you still need to use a 1,000W amp because the speaker is rated at 500W continuous?
This is always a balancing act. Too little power for the application and you can drive the system too hard, clipping the amp input and potentially damaging the speakers. Too much power and you run the risk of damaging the speakers via either a short term peak in the signal or excessive long term average levels, typically via overexcursion or thermal failures, respectively. So the decision is what is the right balance for the application, which includes the abilities of the operators. The 1.5 to 2 times the continuous power rating of the speaker is a good rule of thumb, but it is just that and more a way of determining a viable 'ballpark' figure than it is any design criteria.
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