The woofers may not be compatible between vehicles, even if they're the same size and stuff. Bose has habit of "tailoring" systems. This means not just tossing speakers at a problem and calling it a day. The dashboard tweeters are 4ohm, ~2.5" speakers (Bose actually does measurements in metric standard). The front door woofers are 1ohm, ~7 7/8" speakers. The rear door wide-range speakers are 2ohm, ~5 1/8".
They may switch up impedances for different applications in different vehicles. It's important to note that the speakers out of the Corvette and the TrailBlazer/Envoy are NOT the same. Corvette uses 20.5cm woofers in the C5, while TB/Envoy uses 20.0cm. Noting that these are actually different speakers, there may also be different characteristics such as impedance or wattage ratings. As for wattage, it's anyone's guess as Bose never publishes those numbers. It could be likely that the 20cm standard in the GMT is a different wattage and/or impedance and this is why the one out of the C5 isn't very loud.
And I'd bet you do have the Bose head. 2002-2005 said Bose in the lower left corner of the faceplate. This may have worn off over time, so another way to check is to adjust EQ - Bose only allows treble and bass, while other radios also have a midrange. 2006+ says BOSE on the screen when you turn it on. Unless someone replaced the head unit at some point.