Shyvana is actually a very apt comparison as neither of them have ANY CC whatsoever before 6, and even after 6 they have weak CC (slow, minor displacement). Both are short range, neither have defensive abilities or gap closers pre-6, both are completely built around movespeed buffs to be useful.
The difference is supposed to be that Shyvana becomes a tanky initiator while Eve becomes an assassin. So far, I haven't found that to be the case for Eve. Assassins are supposed to be able to get in quickly, burst down a target, and get out alive. Eve's skillset now is more about sustained damage, which doesn't really work on a squishy character.
When the remake was previewed, Riot posters were implying she would be a great duelist, which I just haven't been able to make work. My biggest issue when ganking lanes is that the AP carry or bruiser just turns around and kills Eve from full HP, even in a 2v1 situation. I jungle just about every character its possible to jungle on, and I've never played a jungler where this happens so regularly. I find her skillset is only good for chasing people down, which only works if they're afraid to 1v1 you. Most people have figured out by now that there's no reason to fear Eve.
Now, she has a mid range Q, W designed for sticking and chasing, E designed for sustained AA damage, R which strikes me as an AOE team fight skill...
Remove the stealth from her old kit. Just say her W is "Stun on next skill or AA." She is a duelist and assassin still.
Sneak through brush/hide in brush>Pop W to setup stun>E for huge burst DPS, stun activation, armor/mr shred for finishing off>AA off sheen proc>Q>AA>R for finishing chase>Q>Sheen procced AA>Kill/Asssist complete, Healed, Ult Refreshed.
That's how she was. That's no longer how she is. And while the developers may maintain that her intended playstyle is an assassin/duelist, the optimal playstyle used by the players according to the meta and other champions in the ring has the potential to be something else entirely.
You want to call her a duelist? Compare her old and new ultimates. The new one is not designed to be used on 1 person (at its maximum effectiveness), whereas the old one was pretty much "focus down 1 person, move on to the next." With the old ultimate, you got steroids to win the duel, and a heal to move on to the next.