The 810 is slightly larger, and thus has a little more space inside. The 810 also has 8 radios, while the 820 must carry 14... yes, it is quite easy these days to cram lots of variable oscillator transistors onto a single main chip, but the radios that must attach to them to make them useful are still large enough to take up a lot more space than the chipset. So, naturally, the 810 has more internal space left over to house a larger battery, as opposed to the 820.
Perhaps they could have made the 820 a little bit more spacious internally in order to house a larger battery, like the 810? I suppose that they could have, but remember that the carrier (AT&T in the case of the 820) gets the last word on what specs they will accept, includin... (continues)