Welcome here, first!
The 3810 is a very nice watch, and the most important, this is a watch you're in love with.
As for Breguet rank, compared to other brands, I'd say that Breguet is a brand to be highly considered when you fall in the world of watches.
Abraham Louis Breguet made a lot for watches, indeed, with some of the most wonderful pocket watches ever created.
Today, Breguet still makes some very nice watches, as the tourbillon Messidor, the 5140 in White Gold with a gorgeous enamel dial, the Tradition, and the Type XX or XXI...
Compared to other brands, I'd say that PP, Lange and some high end JLC watches are on the top, horologically speaking, and in terms of finish.
Breguet is maybe a bit under these 3 brands, IMHO, but a very interesting brand.
Best.
Nicolas