Whether you need a module or not depends on your use case; you certainly don't want to install and enable a bunch of modules that you don't need, as this will slow down your site and can cause other problems.
In this context, if Panels does what you need alone, then you don't need any other modules (and Panels can do so many things that it generally is sufficient by itself).
If you're committed to Panels, there's probably no need to use EVA-- and certainly if you're asking whether there's a need, you should try doing everything in Panels first, as that will be easier to maintain long-term.
EVA would be better if you wanted something more lightweight and just want to make changes for a few things; Panels is more useful if you want to take full control over the layout. EVA can also be used in circumstances where Panels integration isn't finished (e.g., Revisioning module and Panels' node add/edit forms).
That said, these two modules really aren't all that similar. Usually the layout modules are considered to be Panels and Context. Entity View Attachments is really just an extension of the attachment feature provided by the Views module. In that way, you could think of it as competing with content panes, another type of display provided by Views specifically for Panels (for reference, this question relates to the differences between attachments and content panes).