Hi, Andrew -
I have only ever used dry oak pegs, but I think other hardwoods would work well.
I would advise against using softwood; it is, after all, soft. And by using the same species your wood will shrink in the same fashion.
If using green timbers, the wood will shrink around the hardwood peg, creating a super tight joint. Even if the hardwood peg isn't completely dry, it will shrink at a slower rate than the softwood, and not as much.
Anecdote time: There was a guy here trying to de-construct an old TF barn - he couldn't get the pegs out...so he took his chainsaw to all the joinery
. Yes, very unfortunate, but it was constructed with green D.Fir and oak pegs, and was meant to withstand time. (Time, not chainsaws)
*K