These two cameras were announced about 11 days apart in January 2009, and there is very little to separate both of them in terms of features.
They even share the same specifications page on the Panasonic.net website.
From the specs, the only differences are as follows.
Rear LCD screen
The FS25 sports a 3.0” TFT LCD (230,000 dots) on the back, while you only get a 2.7-inch version on the FS15.
Weight
Presumably due to the larger LCD on the FS25, it is slightly heavier at approximately 148 g with a battery and an SD memory card (0.33 lb), compared to 138 g (0.3 lb) for the FS15.
The FS25 is 10 grams heavier than the FS15.
Hand grip
The DMC-FS25 has a prominent vertical grip, while the DMC-FS15 has none. Look at the images below for an idea of the difference.
Vertical grip on the FS25:
No grip on FS15:
Dimensions (W x H x D)
The FS25 is also slightly larger, measuring approximately 97.0 x 57.9 x 21.8 mm (3.82 x 2.28 x 0.86 inch). Compare this to the FS15, which measures 97.0 x 54.4 x 21.7 mm (3.82 x 2.14 x 0.85 inch).
So, the FS25 is 3.5mm taller and 0.01mm deeper. Width is the same.
Conclusion
The differences between the two rest solely in the physical dimension. Get the DMC-FS25 if you prefer a larger 3-inch LCD screen. The FS15, owing to its smaller 2.7-inch LCD screen, is very slightly smaller and lighter.
In terms of pricing, the FS15 retails for around $50 USD cheaper compared to the FS25. Be sure to check the latest prices for the DMC-FS15 and DMC-FS25.