Theoretically the 2 approach would generate the same results, in real world they will be different for the following reason:
1- when you place a trade it is not guaranteed that the broker will really open it. The same when you close it
2- margin requirement (particularly CFD) may lead to totally different number; even skip trades if the margin is too low
3- commission scheme may be different trading a lot or a mini-lot,...

Naturally if you plan to invest few millions it makes sense to spread the risk in several brokers.

Ciao