AP melee assassins have one huge issue that others don't - if they whiff their combo/combo is not enough, they are boned.
AD melee assassins don't have this issue as much because their items ALSO enhance their auto attacks. If an AD assassin whiffs his ranged Q, he can still rely on item amped auto attacks. If an AP assassins whiffs theirs, their autos do jackshit by comparison. AP melee tend to rely heavily on their spells because that's the only thing affected by the items they buy.
Thus, for most AP melee mids, their AP buys ONLY enhance their spells, generally. So, if they miss them or if they are not enough, oh well. An AD assassin's spells get enhanced by their items AND their autos do too, so if they miss spells or combo isn't enough, maybe a few 150 dmg autos will be.
That said, AP Melee burst tends to be up there as some of the highest in the game and their base stats are higher than their mage counterparts. IF the player can play around the range advantage, the ranged opponent is actually at a disadvantage because they CANNOT play "around" the base stat differences.
Take mid lane Diana vs something like Lux. I main Diana, i will spend every single minute of lane phase having to worry about trading my HP for a single CS because Lux can harass me with everything in her kit while i can only throw Qs every 10-6 seconds. If Lux can routinely land Es and autos, she will eventually force me out. If she does this, she can begin accruing an XP lead, which can lead to her being 1-2 levels over me. (example!)
IF she manages, her base stats are now higher than mine; my advantage is gone and her advantage is nearly complete. With a two level lead, there is NOTHING i can do to her alone. She will have too much HP (almost 200 more) and additional damage/effects on her spells and runes.
However, if i manage to only remain even in XP and snag one or two small Tomes, i one shot Lux at 6 with no effort whatsoever assuming i land my spells or don't fuck something else up royally. There's nothing she can do if she doesn't keep me out of her melee range, period. My stats and burst will be too high for her.