Basic rule of I and me: use I as the subject and me as the object
She won't look as outrageous as me // She won't look as outrageous as I
In this case, the correct sentence is the first option because "She" is the subject and "me" is the object
The second option is incorrect because both "She" and "I" are subjects which doesn't work in a sentence. Two subjects need to be connected by a conjunction.