As far as I know the 7820 had the 8.1L in all years made. The 7830 is listed with the 6.8. Both engines seem to have a good rep. We have a Deere with the 6.8 with 3200 hours on the clock and it has been trouble free. It is about 95 PTO hp in our tractor which was the lowest power setting the 6.8 came with. I didn't know till this thread the 7830 had the 6.8.
I just looked and there are 2 Nebraska tests for the 7820, one with the 6.8 and 1 with the 8.1. Both done in 2004. Maybe someone out there knows more about this.
My personal opinon would be the 8.1 due to that is near the bottom end of the motors power output. The 6.8 would be near the top, I just think you will have fewer problems with the larger engine over the long haul.