I'm not sure what you mean by better. I prefer the more precise pull of inertia triggers over mechanicals. Think of it this way: some energy is required to set-up the second sear. With mechanicals, the energy is captured during the first trigger pull. With inertia triggers, the recoil provides that energy after the trigger is pulled. If you could drop out a Browning or K-80 trigger and compare it to a Perazzi trigger unit, you'd see how many more parts are required to make a mechanical trigger work. I shot mechanical trigger O/Us for 18-years before I went to inertia guns and I'll never go back.
Yes, there is an issue of sub-gauge shells not setting the second trigger of a 12-ga inertia gun. This problem is easily solved by changing the inertia block when you get tubes. I've never had a problem setting the second trigger shooting sub-gauge loads in any of my tubed Perazzis.
I've owned and shot both mechanical and inertia triggers including Krieghoff and Perazzi. There is no question the mechanical is more complicated particularly on the K-guns and the P-gun trigger is very simple and reliable. Between the two I believe the Krieghoff has a slightly better trigger pull and is the one thing I missed when I went to the Perazzi.
The mechanicals are IMO better for subgauges because they can be used as they come from the factory. It is possible to swap the inertia block on a Perazzi but that might not be a task that every shooter is up to and would need a gunsmith to do the job.