First off, the naming scheme refers to processors. The iMac G5 and iMac Core Duo are different machines.
As for what you should get her, I suggest the new iMac Core Duo. It is much faster than the G5. However, there are some issues.
Apple has always used a processor architecture different from what Windows PCs use, called the POWER architecture, whereas Windows machines have always used the x86 architecture. I'll spare you the technical details (even I don't get all of them), but basically, they're different, really different.
When Apple introduced the Intel chips (which have an x86 architecture), this created a big problem, as older chips (such as the G5) ran the POWER architecture.
Because of this, the majority of the applications designed for the Mac won't run on Intel processors unless emulation is involved. This is where Apple's Rossetta application comes in. Rossetta emulates the PowerPC architecture (how, I don't know) and allows most applications to run on the Intel chips. Although Apple has ported most of it's own applications (OS X itself run perfectly fine, as well as all pack-in applications), some applications (most notably Photoshop) don't run at full speed on the Intel machines, as they aren't written to run on the x86 architecture.
Still though, I strongly recommend the Core Duo. The speed increase is well worth it, not to mention that almost all applications will be able to run at full speed and not need emulation by the end of the year (these are what are called "Universal Binary" applications. These applications include binary's to run on both Intel and PowerPC machines).