The only difference is you can kill more humans for a given span of time. The end result is the same: Cities are leveled, people are killed. Is it more comforting to have been killed by a conventional bomb than a nuke? I certainly don't think so. So practically speaking, there is no difference.
>Do you believe MAD can exist without nuclear bombs?
Yes. I think you're all vastly underestimating just how much destructive power conventionals can deliver already. You will need more ordnance on standby, but you absolutely can suffer from MAD without nukes.