Assuming that the bias voltages and current sources are noiseless, it won't change a thing. However, a much more important problem occurs if the method 2 is used, which is the need of a control loop to generate the voltages for M1 and M4. If you leave it as it is, temperature, mismatch or corners might force M1 or M4 into triode region, which again might be undesirable for your operation, not mentioning the increased PCB size and more discrete elements. To establish boundries it is possible to leave a margin, but it is going to be a lot larger than the on-chip load solution since you do not cover the mismatches anymore, therefore you are reducing the swing of a so called wide swing cascode.
To sum up:
1- I don't think noise performance will change. Method 2 might reduce noise if noiseless bias is used because it has a lower number of components on the signal path but again there is no such thing.
2- Fundamental current mismatch, caused by operating point difference between the biasing and the real current source will not change as long as method 1 and 2 provide the same voltage.
3- I really do not see any reason not to use method 1. Method 2 is pure blasphemy if Bob Widlar's idea of "Do not try to match IC elements with discrete elements" taken into account.
If you can tell me what brings you to this question, I might be able to help you more because, please correct me if I'm wrong, the method 2 is doomed to fail obviously both commercially by increasing number of pins and complexity and technically by not being able to compensate the effects of PVT.