340 Max Bore

It depends entirely on the block. Typically, max bore for all the small block mopars is .060". I've heard of some being bored to .080", and some that couldn't go .060".

I have a '68 340 block that was bored .060" over for me when I rebuilt it, no issues, plenty of wall thickness. I would suspect that the large majority of them would be just fine at .060" over. I'm also sure that there are probably 340 blocks out there that would be pretty thin at .060". It really depends on the individual block- ie, how much core shift it has, how rotted the water jackets are, etc.

For a street engine, I'd say there's a good chance that either block would be just fine. But, without sonic checking, there's really no way of knowing for sure.