My notes show that the shutter delay on the F70 is 0.4 second.
I have not seen that specification on the ZR1, but the ZR1 is a smaller version of the very popular Panasonic ZS3, which has a shutter delay of 0.6 second.

The Fujifilm F70 has the latest Fujifilm Super CCD sensor.
That should give the F70 an advantage when used in low light (without flash).

With the $50 difference in cost, it would be a difficult decision to pick just one.

Here is a comparison of the two cameras:

Notice there is a green link just under the photo of the F70.
That link will take you to sample photos from the F70.