Well if you like Evanescence, listen to Evanescence and everyone else be damned!
But if you want something like Evanescence but a bit less homogenized pop and a bit more diverse... (Not that I'm too hateful of Evanescence, I think they just suffer a bit from the one concept repeated for an entire album syndrome... Heck I respect anyone who self-consciously alienates Christian rockers)
Lets see here:
I can't come up with anything I would call a direct replacement... Evanescence's torch song meets nu-metal is at least a bit unique. Do you listen to Portishead? They certainly capture the faded grandeur effect that I think Evanescence is going for. Plus Portishead is one of those groups that I think everyone should at least be aware of. For orchestrated work check out PNYC. Plus Beth Gibbons has a voice that, while a bit different, I think you will appreciate.
If you like the piano driven aspect of Evanescence you might consider taking a step back to the early 90s and listen to Fiona Apple's first album, Tidal. It even has an understated gothy classicism.
For strong, clear female voices have you ever listened to Perfume Tree? It's been a while since I've spun up their work... But IIRC they have a similar vocal performance. Again, IIRC Feeler was their best album.
While different sonically, I think it could easily be argued that Evanescence is the spiritual descendant of Garbage. (Or at least that it fits into a similar place in pop culture). Thus they might resonate with you.
All of the above are only somewhat similar either in performance or ambience, but I think they might get you headed in the right direction. There probably are more direct replacements in the goth/metal/alterna-metal world but I'm not really well enough versed to comment.
Edit: Also, you might want to dig a little into Stereolab's discography... A bit different, much more geared towards electronica but I could see a connection.