I have had both the 308 and the 30-30 in Handi's.They both are fine cartridges,but I really like rimmed cartridges in the handi,others will disagree, but I think my most accurate loads have been with rimmed.I use the 125 grain NBT ,in my 30-30 and have had very good luck with it.
I have a very bad right shoulder and cannot take recoil, so the 125's are a answer for me, in the 308 or the 30-30. HTH Doug