Integrated thermometer compared to rod thermometer

The integrated thermometer may already be sanitary-welded into your vessel. The higher price tag is maybe from the significant amount of work involved.

Installing a thermometer yourself involves either welding, or using a weld-less fitting - typically sealed with a silicon washer and thread tape.

What are you using this pot for? If it's a kettle, then the temperature isn't that useful anyway. For water and mashing sure.

One thing to watch out for, is that if you are using this vessel as a Hot Liquor (Water) Tank, the water settles into layers at different temperatures. The water needs to be circulated past the temperature probe for accurate readings.

I doubt accuracy are that different. But these integrated thermometers as you called are way easier to handle, especially when mashing (closed lid). This one you showed is SS, therefore much more robust.

If the brewpot you wanna buy is the one in the picture, then I would guess that this difference in the price is not only due to the thermometer itself+fittings. They put this shinning SS case to make the kettle look nicer.

The very same thermometer in this picture costs 16 euros.

Well, I would buy one SS thermometer, like the one in this picture, and install it by myself.

And if you don't want to drill a hole in the kettle, then you could buy one like this