Why would we simulate baseband rather than passband My question is, Why do we usually use baseband in simulation rather than passband? however, if we want to test our simulated idea in real environment, it must be sometimes in passband !! 

So, should simulation in baseband give the same results if we made it in passband? for term of BER, MSE and so on 

Here is an example as asked in the first comments, 

In baseband, Suppose you have ofdm system, with $s$ is the $n^{th}$ block with N symbol, when performing N-by-N FFT to get $x = FFT^Hs $, after adding a CP as guard interval with length P, we will have $M = x + P$ is the transmitted signal as baseband. 

But in Passband, we will not transmit the $M$ as it's, we will have additional process when having $M$, this process is summarized  conversion --> matches filter --> carrier modulation by multiplying (.*exp(-j*2*pifct), fc is the carrier frequency t is the time period, and them transmit real part of this results, then in the receiver side, we follow the inverse of these steps till getting the baseband signal $M$ then, both passband and baseband will follow the same steps.   

Thank you
One very obvious advantage of baseband simulation of communication systems is the low sampling rate it requires.

Considering a narrowband communication system having a few MHz of bandwidth to a few GHz of carrier frequency, it would be much easier (in terms of computation) to simulate it in the baseband sampling rate.

The reliability and the quality of a baseband simulation depends mostly on how accurate and realistic your mathematical modeling of the actual physical channel and the modulation system using it.