The i3 2100 will be faster, but in terms of the type of workload you list I don't think it'll be $80 faster. Personally if I had an extra $80 to throw into a build like this I'd rather spend the money on a 40-60gb SSD as that will give you the kind of day to day performance increase you want. Windows will boot up faster, applications will boot up faster, and all that. The mechanical drive is the bottleneck in modern PCs.
Plus with the A4-3400 you get ATI graphics and more importantly, their drivers. The HD 2000 graphics isn't bad, but the drivers are horrible. I've been using a 2100T in my HTPC for a while and the latest drivers have been a nightmare for me on windows 7 64-bit home. Even surfing the web I wind up with my TV flashing. It is an issue with the last 2 or 3 driver releases, the previous ones were fine. But I just went back to using an HD 5450 for the sake of my own sanity. Other people may not have that issue, but ATI and Nvidia have much more reliable drivers, more feature rich panels, and much more regular updates.
On the note of Biostar, I've had generally good experiences. I have a biostar AM2+ board running in my 2nd server along with an X2 250 and it has been reliably running ubuntu for the last 2 years or so. Never had a single issue with it. But I also had an LGA 775 Biostar board go bad on me. The RMA process was unique to say the least. First email never got a reply so I called them. The cleaning lady answered the phone and told me the technician was at lunch, so she left a postit note on his monitor for me. The guy called me back a few hours later and I had my RMA in the mail shortly after. I tend to think of an RMA department being more than 1 guy, but I got my board replaced. They are not my first choice but on a budget I can't complain.
If you feel you need the performance in other areas, such as for video editing, encoding, or heavy photo editing then the i3 offers that in spades. But if firefox, an email client, and a couple of documents are the extent of your workload then I personally wouldn't bother spending the extra money.
Hell if it was me building an office PC for that kind of workload I'd probably go with an E350 based system with an SSD. It would be slower than the A4, but also extremely small footprint being mini-itx, extremely low power (sub 30w max load), and you still get great graphics. The 1.6ghz dual core is nothing special, it'll out perform an Atom but any of AMD Athlon or newer dual cores will be faster in general.
