+1 for what Rick said.
Additionally, the PTAC (or thru-wall unit) will normally impinge on your space more than a high mounted split system. You will also have choice of greater performance capacities with the split system, some of which are as large as a two ton system.
The normally lower mounted thru-wall unit may be more of a challenge to maintain due to the proximity to the ground - filters get dirtier, shrubbery obstructs airflow, snow buildup prevents operation, etc.
Plus, the wall sleeve for a thru-wall unit requires a large wall penetration that must be framed in, a requirement that does not exist with the split system.
As well as being quieter, I think that the better split systems are of a higher quality than the better thru-wall units. I suspect they have better operating efficiencies too. Note that I am not talking about some of the newer Chinese units which I do not recommend.
It should be noted that estimated equipment service life is 10 years for the PTAC, 15 years for the split system.
As always, offered only as opinion