If symbols of EsNo_ were transmitted through AWGN environment, which is (noise = sqrt(1/EsNo_)*(randn+i*randn) where Es=1), the low EsNo_ would increase noise.
Thus, in AWGN, OFDM has worse BER performance.
Re: What is the difference of OFDM in AWGN / Multipath fadin
AWGN is more like a mathematical fiction. it is only good to use when you are only considering the thermal noise. it doesn't account for the fading. Furthermore, you don't need use an equilizer, if you are using AWGN.
AWGN is a model, used for simulation. it is not real. it depends upon what you want study/simulate. if you want study performance degradation caused only by thermal noise you should use AWGN model. If you do want study fading effects, you can use use other mathematical noise models such as Rayliegh Fading Channel which somewhat close to the real environment.
And yes, if OFDM would have worse performance in an awgn than the non-ofdm system because of CP. And Even you remove CP, then the OFDM and Non-OFDM system would have same performance.
OFDM is used to counter Frequency Selective Fading. So, it is advised that you use Rayliegh Fading Channel.