Good question. The real answer is maybe.
Theoretically you would think inspected boats should be "safer" because the USCG has inspected them and found them to be mechanically seaworthy and the crews have in many cases been required to show their proficiency in simulated emergency situations. But there are always people looking for the easy way out and a multitude of ways to put lipstick on a pig to pass an inspection.
Are 6-packs less safe than inspected boats? Not necessarily. Most reputable 6 pack boats make a large investment to upgrade and cary extra safety equipment. The captains running them are extremely professional, knowledgeable, and take great pride in their vessels and their operation. The reputation of a boat is usually pretty well known and easy to verify. That being said, there are plenty of 6-pack boats that only due the minimum. No O2, no EPIRB, minimal cheap life jackets, all the cheapest approved stuff they can find to be legal, and they will have a reputation too. Just not a good one. But inspected boats do have the same issues on occasion.
The 6-pack guys are licensed as required and honestly the USCG testing is not that different between 6-pack and 100 ton, which is what a lot of the larger boats are licensed as. The sea time requirements are a little different as one can have time on a bass boat on a lake and qualify for a 6-pack. Sea time for 100 ton licenses generally requires, and is usually obtained, via a more commercial route and is a more verifiable sea time. There are always people who are going to fudge the sea time requirement but that happens for both licenses.
Inspected boats cost more to run, require more gear, and of course go through inspections. Fire, abandon Ship, and Man Overboard drills are supposed to be done and logged. Sometimes the USCG runs these drills during the inspection process. Drills can and do get pencil whipped though. If an inspected boat is just going through the motions, is it really safer? Just because they passed an inspection doesn't necessarily mean that the boat is safer. Maybe the inspector missed something. Inspections are really spot checks, the entire boat is not truly inspected.
If I'm at the dock and looking at a boat to possibly charter I immediately look at the condition of the safety gear and the tidiness of the boat. Divers can beat the hell out of a boat so that cosmetically it looks bad but the safety gear should be in good operating condition and the boat should be clean even if it is beat up. Is the safety gear stowed in an accessible spot? Does the boat look kept? Does everything have a place? Those few things say a lot about how a captain takes care of his boat. I also look at the mooring lines. It may just be my pet peeve but there's an old saying about "know a sailor by his lines." Ratty lines in my mind lead to a ratty engine room. If you're willing to let that huge investment be secured to the dock with frayed unkept lines, how do you treat your engine room?
If I get on a charter, I listen to the brief. A well run boat with a safe crew will give a good brief. The safety brief should be done before the boat leaves the dock. At a minimum you should hear where the life jackets are located, where the fire extinguishers and first aid kits are, and what to do if you see someone fall over the side (not on purpose). You should also be told to let the captain or deckhand know immediately if there are any injuries or if you observe something that could compromise the safety of the passengers or vessel. The safety brief may lead into the dive brief but should always be the first thing. Unprofessional crews do not give good safety briefs.
When you start looking for a trip, go research and read reviews on line. Yes, reviews can be manipulated but usually, overall, you can get the general idea of what to expect. Web sites with wrong information, the wrong definitions or acronyms, and crazy long liability releases that release the operator from gross incompetence and other such craziness give me red flags. It's a business, if you spend time and effort on your site it will lead to the impression that you spend time and effort with your boat and trips. Again, thats just things I look for. Sometimes people aren't computer savvy or they have all the business they need and the website is just an after thought so a bad website doesn't necessarily have to mean an unsafe boat.
After all this I don't think there is really a greater risk for day trips on 6-pack vs inspected boats. Actually, I prefer 6-pack boats. I don't feel safer because an boat is inspected or not inspected but rather how the vessel is kept and run. I'm comfortable on boats, don't need a lot of help, and I like the more personal feel of the smaller vessel. There are also less other people to deal with which is always nice.
Good luck on your trips. Listen to the briefs. Ask questions if you don't understand. Relax and enjoy your charter.
Safe Diving.