Might as well assume the labs are using the same chemistry. This then means they may have their computer, the one that reads and reports the raw data, are set differently.
According to one Soil Science Society of America text, soil test results are an index not a discreet quantity.

The labs will no doubt tell us differences are from sampling errors. This is only a partial truth. The location of each probe site can have a drastically different result. This is simply the nature of soil. It may look uniform and homogenous, but it isn't.

To find if or what fertility element is limiting production I suggest you pull tissue samples during the next season. The nice thing about tissue sampling is there is less differences between labs with tissue testing than with soil testing. The difficulty with tissue test is it will tell you what the most limiting element, if any, is the problem. Cure that and the next limiting element will make it's self known.

In my case I found copper was deficient. Cured that and Molybdenum became the deficient element. Cured that and then finally found potash was deficient, on ground that three different labs found 300+ ppm K. Later on the rather drawn out learning curve I learned of the effects of a high to excessively high Cation Exchange Capacity. Turns out if I work with my CEC it is not a problem but an asset.

There a multitude of factors that can effect production. Your top or sub soils may not be as deep as you neighbors. You may be enjoying a more sandy deep soil, a rocky deep soil or a heavy clay deep soil all of which  may not be to your advantage.

Another avenue to explore is to do some deep probing. Some years ago NRCS used their truck mounted long probe and pulled 4 foot long probes for me. That is an education seeing 10 probes laying side by side in the back of a pickup. There were obvious differences to the naked eye.

Lastly the fields you have may be better adapted to growing a different crop. Something with different root system and or growing habits.