I wouldn't try to do both of them either, and looking back at a previous thread of yours, no more than 3 locations seemed to be the consensus among most posters.
The CT makes the most sense location-wise because it can be plugged in between Venice and Rome where the AC is going to involve backtracking (if you're flying into Venice and out of Rome). Both are going to be very, very busy but you may feel mob effect more in the CT. The trains, ferries, villages and open sections of the Sentiero Azzurro trail system will be packed like sardines, and especially so depending on size/number cruise ships possibly docked in La Spezia those days. However, if you are hikers, you can escape the worst of the masses by hiking some of the lesser-used trails extending higher into the hills, and a big chunk of the day trippers will leave in the later afternoons.
The SITA buses and ferries around the AC will also be packed, and the archeological sites (if you are thinking of doing them) at Pompeii and Ercolano will be brutally hot. Still, Sorrento has more room to accommodate more bodies so it's really a tossup?