Diana is better than Akali in every single way
They are both assassins that go in and have no escape unlike Fizz, Kata, Ekko, Lb, Riven.
They are also played the same way, Q then R to the target.
While Akali has a shroud that gives her worthless movement speed, Diana has this low cd shield that deals damage and refreshes itself. Sure Akali is hidden for a while but she doesn't get bonus resistances inside her shroud. I honestly would prefer a shield that reapplies itself instead of being invisible in a small area taking skillshots for days or screwing myself if they have an upgraded red trinket/pink.
While Akali has to depend on energy costs, Diana has mana and barely needs any manaregen. If you disagree about her low manacosts, check her core build: http://champion.gg/champion/Diana
Their Qs have the same cd except Akali's Q isn't AoE, has lower range and deals far less damage unless you trigger it by AAing with your cute 125 melee range. Btw, Diana has 150 range.
Diana's R is a better version than Akali's R, I'll explain why.
If Diana doesn't Q before hitting R, the cd of her R is the exact same recharge time of Akali's Rs (recharge time= time to get back another stack) so in this scenario, Diana using her R is like Akali using her when she only has 1 stack like when she just reaches level 6.
If Diana uses her Q before R, the cd resets so Diana R = Akali with 2R stacks. Since her Q has a relatively low cd and she has her W to tank damage for a while (like I said before, her shield gets refreshed) , she can wait for it before using R again for an infinite stack of Rs.
What's more, Diana's R has a higher range than Akali's R and also deals more damage.
Thinking that Akali's R is better because she gets 3 maximum stacks is a noob trap because every decent high elo player will be able to QR with Diana in a second and always keep his ulti off cd when needed.
So Riot please do something about Akali because she's been gutted in January and she's still as bad as ever. There seriously is no reason you should play Akali over the other assassins that have escapes or even Diana who's in the same category.
If anyone wants to confirm what I'm saying about the cds, damage, etc: