They should not cut our sooner, as they differ in bandwidth allocation, but not the power of the HD signal.
They definitely do, and it's a trait I've observed on multiple stations in different markets. For example, the public radio station in Pensacola, whose transmitter is southeast of the city in Gulf Breeze, has an HD signal that I can pick up dropout-free almost all the way into the middle of Baldwin County Alabama, a distance of about 40 miles. But the HD3 will start to experience dropouts right at the state line, which is only 25 miles from the transmitter. It never cuts completely out, but it becomes unlistenable much quicker than the HD2.
The same thing happens with iHeart's HD transmissions from their Spanish Fort tower in the Mobile market. Both WRKH and WMXC have HD3s running lower bitrate talk formats, and both cut out noticeably more than the HD2s. I'm only about 18 miles from that site and walking around the house it drops out constantly, but only the HD3.
I've noticed this both on a portable Insignia FM-only radio and an OEM Mazda car radio, so I know it's not just one particular chipset's quirk.