Vol:
If its done correctly, I think you will find its 6 of one, half-dozen of the other.
The ONE caution I have encountered with the "steel fix" approach is that as the wood shrinks and swells with changes in humidity, the steel may have the opportunity to get loose in the stock, whereas the wood dowel will ( theoretically) take on or give off moisture at about the same rate as the surrounding original stock material, thereby remaining "tight". I have no idea if this is a real concern, and I do not have any experience with the steel rod method, so I cannot tell you firsthand.
I have used the wood dowel method to repair the fragmented stock of an 1840's era muzzleloader but I have not shot it since the repair. A friend who frequents this board, Doc Bill, has used a plywood insert to return a badly battered and completely broken and shattered early Lefever stock to service. He shoots the gun a lot, and it works.
On the other hand, Friend Petrov, as demonstrated above, knows what he is doing and uses the steel rod method.
So... my guess is use whichever method is most convenient, just do it right and make sure the epoxy is mixed correctly.
My thoughts, anyway.
Regards
GKT