General answer: MF was intended as an ADC hence going AD is more crucial, but AP MF is an unconventional build on her. Her ult scales well with AP but it's actually AD.
MF is a champ with no hardcore CC or reliable mobility in addition to her squishy ranged nature, so it's safe to concur that damage is the best way to go for MF. The thing that makes AD MF does more damage to AP MF is probably her ability for follow-up actions. MF scales well with attack speed with the additional damage from W passive. Like all ADCs, her damage is a big deal, but in order to apply huge damage she has to be in a good position and able to do damage without much disruption.
Now as for AP MF, she does have scaling in AP, but in the end, almost everything resulting in physical damage (Q-R). Her E (Make it Rain) seems to have very good scaling, but enemies rarely stand under it full duration, leaving it like an incomplete Morgana's tormented soil. While Q sits at a low cooldown at maximum skillup, she's heavily depending on Lich Bane for that proc damage – meanwhile due to low attack damage and attack speed, the time waiting for next double up is just wasted while AD MF can even ignore the use of Q and just go straight for crit-basic autos. Let's not also forget the fact that her Q has a really short range as a spell for MF to go in and be in a vulnerable state.
End gaming, AD MF scales like an ADC, while AP MF probably falls off when enemies get more HP or MR.
I still like to see people use AP MF, it's always fun to watch =]]