I've owned both of these cameras, and returned the DX6490. My reasons have been posted several times both here and at Phil's DP Reviews Forum: http://www.dpreview.com/forums/forum.asp?forum=1033
so rather than repeating myself, may I suggest you do a SEARCH in both forums for DX6490 and my name "Charlie Howard" or "Charlie+Howard".
With regard just to the indoor capabilities of the two cameras: both of them have problems indoors unless given some help. In fact, one of the main reasons I returned the DX6490 was that it's indoor pictures were very inferior to identical pictures taken at the same time with my older Kodak DC290.
* DX6490 *
The DX6490's viewfinders do a much better job in low-light than the FZ10's, but that only helps when composing the picture, not in recording it. Normally, you wouldn't be trying to take pictures in a room so dimly lit as to make the FZ10's viewfinders unusable, so this is more of a "bragging rights" issue than a real world one.
Without a flash, the DX6490's images were so underexposed as to be useless; with a flash, they were still a little underexposed, but the colors were off because the room lighting threw off the White Balance. There's really no way to get around this problem on the DX6490: you can't do a manual white balance to correct for the yellow-orange room lighting that creeps into a flash picture, and the DX6490 does not have a hot shoe (I don't recall whether it has provision for a Sync control). Eventually, you will realize that you will either have to use an external flash or just not take any indoor pictures; but by that time, it may be too late to return it, and you may be stuck with an unusable camera. Although there is no hot shoe to hold a flash, you could use a Slave flash, but would have to get a handle/bracket to hold both the camera and the flash.
* FZ10 *
Without a flash, when using Auto ISO, the FZ10 can take an adequately exposed picture indoors with reasonable room lighting, but the camera usually will select ISO 400 in that situation, resulting in a VERY noisy image. The image quality will be poor, even if you go to the time & trouble of running it through a noise reducer like Noise Ninja or Neat Image; and facial details will be lost. My 200 Thanksgiving pictures fall into this category.
Without a flash, using ISO 100 (the highest level that yields a fairly clean image), the images on the FZ10 will be badly underexposed. This can be corrected with a photo editor, but you'll also have to correct White Balance unless you used the camera's WONDERFUL manual WB capabilities (something that is far weaker on the DX6490). Some of my Christmas pictures fall into this category; the rest, into the first category.
At ISO 50 or 100, the camera's built-in flash is very weak, as you already know. Using an external flash can solve this problem, but will take some experimentation to find the right combination of settings on the flash and on the camera. My January-February pictures fall into this category, and although I'm closing in on a good solution, I'm still not there: I want to be able to use ISO 50, but even with the blindingly powerful external flash I'm using now (the fourth one I've tried in three months... each more expensive than its predecssor), ISO 100 is the slowest that yields pictures that do not require post-processing.
BTW: my "test" pictures that use indoor lighting, but don't have people in them, come out a lot better than "similar" pictures of people, expecially of groups (the distance has to be greater to fit them in).
* OTHER CAMERAS *
This indoor illumination problem seems to be more common with many digicams than I realized when just using the DC290. The DC290 is only a 2 mpx camera, and the pixels on its CCD probably are larger than on current 4-5 mpx consumer digicams, so it can shoot at higher ISO's without introducing excessive noise.
Over Christmas, I borrowed a friend's Canon Digital Rebel, equipped with a 28-135mm Image Stabilized lens. This is truly beautiful equipment (and heavy), but much to my surprise, its pictures were not as good as the FZ10's. Indoors, it's built-in flash underexposed the images just about as badly as the FZ10's. The Canon's images had less noise (it has a much larger CCD), but the pictures were dark, flat, and improperly white balanced; the FZ10's were only dark. Both required serious post-processing to make them usable.
The fundamental problem, in my very amateur opinion, is that none of these consumer-oriented cameras is physically large enough to hold the large capacitors needed with a powerful built-in flash. They could be built that big, but presumably the manufacturers have found that people don't want to buy such bulky cameras.
If you are determined to not use an external flash, you may want to look for a digicam that can minimize noise at ISO 400, or else find a way to make your room lighting bright enough for the camera you choose.