I have a question. What choice is better for feeding a Mosek solver? 1- High number of constraints (for example 10^7) and low number of decision variables (x) (like 10), or its dual equivalent with low number of constraints (i.e. 10) and high number of decision variables (10^7)?

Is there any difference in the convergence speed?
Which of them is better in terms of MOSEK restriction (2^31 entries at each moment)?

By this you mean that CVX intervene in the performance of MOSEK solver to convert the primal problem to a dual one in some situations? If the dual one is easier to handle.