Beginner level : Bit error rate trend
A lower BER would seem to be better, who wants corrupt data after all?

However, it's like the bankers' (apparently) mantra that 'if you are not cheating, you're not trying hard enough'. If in a working comms system you have a BER rate much lower than your correction can handle, you are operating the system with too much power, or too few users per cell, in other words with an inefficient use of resources. The power control algorithm of most modern comms systems reduces the output power (in the mobile to save battery life, in the base station to reduce interference to other users) when the receiver reports back an unnecessarily good BER.

Error correction/detection systems allow you correct small numbers of errors and detect and resend blocks with large numbers of errors. This enables the system to achieve effectively zero error when appropriate (file transfer) and tolerable error when it doesn't need to (speech, video). 

Now to your actual question.

If your measured BER is better than your theoretical? If 'theoretical' means 'best possible at this SNR', then someone is not comparing like with like, they've modeled the best case wrongly, or tested a subtly different system. If it means 'target level for economic operation of this system', then it could easily measure better.

Low SNR is where systems have a BER problem, and where the equaliser earns its salt. As the system is not striving for zero BER, it may be acceptable for a worse BER performance due to the equalizer at high SNR, as long as it still meets the system acceptable BER level.