EEO's are valuable - but you need to compare a discount rate x2 against the generally available rate x1.

Say the EEO rate $150 for Friday night. Then Sat night is free and gets no point credit towards your night count for elite status. Thus only 1 night.

Say there was a special AAA rate for $85 per night - so that is $170 for the two nights, and you get two nights credit towards elite status.

Also - you need to watch for rates that include parking and other features. Say parking is $25/day - that's $50. You need to factor that in as well.

While the EEO rate x1 will generally be better (since it is still a weekend), you do need to make the tradeoff.