Other things you are doing in your code are likely to dominate run times. We would need to see your particular application to offer better advice.
Linear indexing for calculations and assignment might be slightly faster in the background, but I would be surprised if you could even tell the difference with any testing you could do.
Memory size is the same.
The pros & cons of one vs the other are entirely dependent on how you would be accessing and using the data downstream in your code. Note that for a full matrix M, the espressions M(:) and reshape(M,N*M,1) both result in shared data copies (i.e., no deep data copy) and are extremely fast. So you can work with both simultaneously downstream in your code depending on how you want to access the data. And, even if M is a 2D matrix, you can still use linear indexing on it without even reshaping it first.