In terms of Dominion, the reason why she could be played so effectively in the right team compositions, was because of her ability to be played as a roamer. You could show up anywhere on the map, blow up champions at 20-50% HP as an AP nuker or shred enemies down in seconds as an AD/AS character. Their inability to know your coming, or that your even about to engage in that 1v1/2v2 etc, made her powerful. She had total map presence, which was difficult to gauge in terms of power, but made her effective on the map, where she could safely turn the odds in favor of any single engagement.
The new changes take all of that away.
In Dominion, lanes are small. Presently, Eve is able to wade past the battle lines, and get to that retreating Teemo headed for a health shrine, nuke/shred him to high heaven, enter the bushes and be re-engaged in stealth and headed for bot all before the enemy knows what happened. Now those lanes have become death traps. Her stealth detection radius will like be small enough to not safely run through a lane and engage low health champions (conversely her hate spike hits more targets and her nuke does more damage), but this means that she will no longer reprise her role as a roamer. Your going to play her like any other melee champion. You can still roam, you just will not have the power you had before. You will still be able to turn some tides of battles like you could, by showing up unannounced, but stealthing to the back of the line to nuke that low health Lux? Not happening.
Shes going to play differently. A lot differently. And you will probably notice it. Conversely, looking at the changes, she could be an excellent bot or still have a lot of use at top.
Why? Hatespike is smarter. It will first target a) the target you are auto attacking b) champions c) low health targets. Its now a much smarter projectile, and it hits more targets (perhaps up from two, to three) and it has even more range! This could make her an absolute beast in team fights, a long with her aoe nuke slow for engaging enemies (and possibly some serious defense boosts for slapping a couple champs with some dps).
The difference being, you will play her more like other AD/AP melee types.
On bot she could see some play. Why? Hatespike again. Depending on how powerful the new iteration is (Perhaps an AP build with CDR, the cool-down was increased to make up for the increased targets and damage), she could now be more adept early on at clearing and pushing lanes. Her passive stealth and nuke could allow her to trade effectively and control the health shrines, setting herself up for a nuke and chase to kill (lot of movespeed potentially).
Just some ideas after reading through all the riot posts on Eve and ruminations on how she might be played in both aspects. Theres some positives, and some negatives. The key thing to take from it is shes simply going to change in how you play her. Her role of roamer may be over in favor of a strong, melee assassin (Which was apparently intended).