The technical specs are as follows:
F31: 6.3 megapixel, 3x optical zoom, �120
A825: 8 megapixel, 4x optical zoom, �90
Based purely on these figures the A825 is better, but there may be other factors to consider.
The A825 is a "new" camera so may have more up to date technology.
Also the A825 is slightly bigger if size is important to you.
The F31 has a lithium ion battery whereas the A825 has 2xAA batteries.
If you buy the one with AA batteries you may have an extra cost of buying re-chargable batteries and a charger.
I think Lithium Ion are better because they they hold more of a charge so you can take more pictures before recharging, however a camera that takes AA batteries means you can go into any shop to buy new batteries (but they may not last long).
In the end the choice is up to you.
You can compare the cameras here:
http://www.fujifilm.co.uk/digital/cameras/inde x.php?tnav