Which one serves as a better assasin type character for mid-late game and why?

Akali.

Her inivis circle slows... more CC than Kat .

Both require to be fed to be much use in any fight.

Akali jumps in two shots Fiddle invisi circles out.

Kat waits for the fight to be nearly finnished then ulti's... getting a triple kill.

Hmm ok I guess it seems like Kat would be more useful but I think It is easier to get fed as Akali than it is as Kat.

Fairly similar basically which gets fed more. Kat can farm easier earlier. Akali can pick off squishies easier as soon as she hits 6.

Kat: Much stronger lane presence until level 6, in which case her ult is hit or miss against her enemy.

Akali: Moderate lane presence before level 6, when she dings, she will kill someone in her lane if played right, snowballing from there.

Both if fed wreck teams, both jump into the fight late, Akali is a better chaser, but Kat can pull out easier and has better harass...
Akali's more "I burst your face" while Kat is "I'll work you down till I can kill you"

Pick one that fits your playstyle, all I can tell yeah.

akali is better in high elo as she is not hard countered by a single stun.

Kat is a pretty weak champion imo. She needs to get fed to do well, she gets hard countered by any cc or tanky teams, and she has absolutely no cc. At least if the enemy team is heavy on stuns/tanks akali can suicide dive the enemy carry and still do her job.

Definitely Akali if by assassin you mean someone you can rape a squishy carry.
If by assassin you mean someone who can just straight kill then its much closer.
Also, Akali is much tougher to counter than Kat

Kat pretty much

she contributes more to a team with some stuns, and has decent escapability.

Akali on the other hand, either relies on flash or team help.

I much prefer Akali but I think she definitely requires the player to be more careful about when and where they pick their fights as she has no escape without shroud or flash available, and flash alone often isn't enough to get away (shroud often is if you're a good juker but that means you have to save energy for it). She also doesn't require a few seconds to channel an ability to do any real damage. She also has the ability to stay in a fight hiding under her shroud while regaining energy, which makes it so much easier to stay near those low hp champs and take them down especially 1v1. I've gotten countless kills when near death because I could hide next to them while gaining energy for the last combo, where a kat would've already had to disengage to wait for cooldowns.