Are commercial pilots likely to do a better job than a PPL - yes, undoubtedly, they are more current and their training more focused.
....Is a statement which is extremely arguable, and probably has little basis in fact. The "better job" will be done by the person who has the better attitude overall. The letters printed on their license will have, at most, a passing relationship to this.
My experience has been that a conciensious PPL owner is every bit as likely to care for his aircraft, flight, and passengers, with the care of a CPL. In my days I have flown with many CPL's who were very "wet behind the ears", and probably more dangerous, because they had been annointed CPL's and wer now magical. Three of them managed to kill themselves, in aircraft which I, a meer PPL at the time, had sucessfully test flown with no problem. There I am, the PPL, trying to explain to the investigator how the magical CPL could not keep the plane under control, and the flight within his skill set. It was not the fault of the plane...
On the other hand, I have known many PPL's who said "I fly within my skills, and don't fly in xxx conditions, because it is beyond my skill. They have flown safely for decades, and have a safe attitude.
I flew 33 years and 5500 hours as a PPL, obtaining my CPL last summer. Aside from how I sign logbook entries, I'm not doing anything differently now as a CPL, than I did as a PPL.... Maybe I'm safe, maybe I'm not, but I can endanger people for hire now!