I have two water temp gauges on my 261-powered 51 3800. One, the original gauge is in the standard location between cyl 5 and cyl 6 on the manifold side. The other one is in the water outlet neck below the t-stat. The t-stat location gauge always runs hotter than the one in the head. How much hotter depends on how hard the engine is pulling. That could be because the sending unit is a little off or the gauge head is off or that there is enough resistance in the 3-way switch for the various sending units to throw it off; engine oil temp, water temp, and aux. transmission temp. Or the water at the outlet to the radiator is actually hotter. I mostly water the factory gauge.
Over the years I've seen three Chev sixes with burnt pistons, two number 5 and the other number 6. Maybe the military was on to something when they speced the 270 and 302 engines with the bypass pipe.