On the thread Cal POLY SLO Engineering Admission rates for 2018 @Gumbymom explained you can take the take the FTF (full time freshmen) Target # and multiply by 3 since a ballpark estimate for yield is 1-out-of-3 and divide by the FTF apps to get an approximate acceptance rate. That thread was for 2018, more recent numbers are at https://content-calpoly-edu.s3.amazonaws.com/ir/1/images/NOT%20ADJUSTED_AGGREGATE%20-%202022-23%20Enrollment%20Projections.pdf
Doing so gives a guess of Aerospace admission rate being about 12% and MechE being about 20%. The catch, though, is neither of these rates actually apply to him 
Read up on the “ecological fallacy” about applying group statistics to individual predictions and you’ll know why.
As for which is better for rocket propulsion, my guess (as one not in the field) is either is fine. For one thing your son may not understand the full scope of what engineers working in that area do. Some work on the actual fuels, some work on the plumbing delivering the fuel (when liquid), some on the structures inside the rocket holding the fuel and other elements, some on the hardware making up the valves controlling fuel flow, some on the control systems adjusting fuel flow and burn rate, some on guidance so the darn thing goes where you want, some on vibration analysis so it doesn’t shake itself apart, some on aerodynamics so the atmosphere doesn’t pull it apart, and so on. The odds that he’s informed about all of these and has made a careful choice about fit and career prospects may be low. It may be that aerospace or MechE is a better fit for some of these than others but perhaps it’s too early for him to know.