Relationship between Nyquist and Shannon channel capacity
Well, I think both are unrelated unless you have some constraints. 

The Nyquist channel capacity says you can transmit $2B\log_2(M)$ bits per second for given channel bandwidth $B$. It does not say if these bits would be received reliably at the receiver in the presence of noise or channel distortion. I am assuming here that bandwidth limit is imposed by channel. Your transmitter can afford to have higher bandwidth but channel does not.

The Shannon Channel capacity theorem says, in order to receive the transmitted bits reliably (that is Probability of Error $\text{P}_e \rightarrow 0$) in the presence of additive noise, the maximum rate at which you can transmit is $B\log_2(1+\text{SNR})$ bits per second.

So if your requirement is reliable communication and the channel has a bandwidth limit of $B$, then $C_n \le C_s$.