Akali and Diana are as different as...wait for it...NIGHT AND DAY.
That didn't even work, but it was very in the spirit of Diana. But the point is they are very different.
Diana and Akali have a pretty similar pre-6, although diana's is safer if they do not buy a pink ward. If they don't pink you pre-6, akali is quite easy. Diana can stay in the lane a bit better due to her shield mitigating some harass and her long range cs ability, but akail can last hit pretty well with q and not push the lane, and use her shroud on the tower to get near perfect last hits. At 6, akali is 200% scarier than diana, simply because you cannot dodge any of her damage, you cannot ever flash away, and her spell vamp is likely coming online, meaning harassing is not going to be a means to control her anymore.
The thing about akali is she gets all this free gold from her passive, and it scales with itself. Akali can build pretty much any damage item and it will still be pretty good because of the bonus scaling she gets. Of course hextech gunblade is just kind of awesome for akali, as it gives her the CC and burst to kill pretty much anything, on top of being incredibly stat efficient- akali ends up with like...30+ spell vamp from that one item, and bonus AD, and 16% bonus damage on hit. But the thing about akali is you have options! Lately, I am in the habit of going Hexdrinker into pistol, simply because an Akali with a hexdrinker can simply never be stopped early game.
Akali normally builds into AP, so not only does her massive spell vamp just get scarier, but her auto attacks just keep becoming more dangerous- It isn't uncommon for an akali to reach the point where every auto does an ''auto-crit'' of spell damage equal to that attack.
Diana doesn't scale nearly as well- frankly, I don't find diana scary at all past the midgame, whereas akali will always scare me because items do so much on her. Diana get's one shot in the fight to hit her target with Q, and then she has to wait again to actually burst someone down. Akali just jumps on your carry...then jumps on him when he flashes...then jumps on him when you try to peel her...and then he is dead. And then akali gets another charge of her ult, so she leaps to the next lowest person..then the next...and before you know it, PENTAKILL.