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That' not how the comparison function for Array.sort() works at all: it should return negative, zero, or positive.

Eating up all or part of the props argument (due to your array.shift() call) is bad practice.

The usage is cumbersome:

array.sort(function(a,b) { return comparePropsOfAWithB(a,b,["a","b","c"]) })

Wouldn't it be nicer to write a propertyComparator(…) function that returns a function?

array.sort(propertyComparator('a', 'b', 'c'))

Something like this:

function propertyComparator() {
    var props = arguments;
    return function(a, b) {
        for (var i = 0; i < props.length; i++) {
            var aProp = a[props[i]];
            var bProp = b[props[i]];
            if (aProp < bProp) return -1;
            if (aProp > bProp) return +1;  
        }
        return 0;
    };
}