I am having a custom .30-06 built on a Howa 1500 long action Stainless Steel.
I still have to choose a stock and I have two options: Hogue Realtree Hardwood FLBB or Bell&Carson Medallist FLBB Realtree Hardwood.
Which of these would be the better choice?

You asked for opinions, so here's mine-

I have both stocks, though not in that camo pattern. If I were having a custom rifle built I would use something a bit better. Don't get me wrong, I like both stocks but I'd consider something a bit more, ah, finished for a rifle like that. If this is a stalking type rifle I'd use the B&C first choice over the two. The Hogue has a bit fuller grip if you have smaller hands you might like the B&C better as well. If you were building a varmint rifle I'd probably suggest the Hogue first, but again this is just my opinion.