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A cap-weighted index like SPX means that if AAPL moves up 3%, the bottom 14 companies could go to zero, poof, out of existence, and the index will be unchanged.
An equal weighted index means that each stock comprises the same percentage slice of the index value. Presumably for SPX this means each stock is weighted 100 percent / 500 stocks => 0.2% each. If AAPL is up 3% and WYNN (worth 300x less than AAPL) is down 3%, these two cancel each other out and the effect on the index is zero. However, if AAPL is up 0.1% and WYNN is down 3%, the index value will be lower.
An advance/decline is a binary up/down, so whether AAPL is up 0.1% or 5%, it just adds a "+1" to the advance/decline value. So, they're equally weighted, but *how much* they're up or down does not affect the advance/decline value, whereas the amount up or down does affect the value of an equal weighted index.
