My first thought was the this is pretty well standard with the newer low flush, or two flush toilets as I call them. This is because the way they flush with less water is to make the internal bowl and siphon section smaller in diameter, thus they clog easily.
However as these seem to be older toilets, there could be a few different issues.
With the lid off flush the toilet normally and see if all the water drains out of the tank. Flush again holding down the handle, forcing it to drain all the water. Any difference in how it flushes could indicate the flapper valve is not staying open long enough. This is a common problem and the easy solution is just to hold down the handle until the flush is complete.
The second common problem is a clogged roof stack vent which will starve the toilet drain of air and it will not flush properly. In my area this happens often as squirrels and birds like to sit up there in the warm exhaust during the winter and they drop various things in which can eventually clog the vent.
Also are you sure there is nothing in the toilet, the most common things I find are tooth brushes as no one wants to fish them out. They just think they can flush them away, problem is they only flush them around the bend and they will never actually get out of the toilet, just sitting around waiting to create log jams.
I don't work for Stockcharts, I'm just another user always trying to learn more and willing to share what I've already learned.
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