Here's some options. Depending on your license level and how many and how big the differences are you may like one or the other.
One method. If you can convert your polygons to lines and points, then you can select the lines in BreedBlocks that need to be replaced, delete them, and copy and paste the Boundary layers lines in that area into BreedBlocks. Extend or trim any intersecting lines as needed and/or use planarize and delete the unneeded extensions. Then build polygons using the points for attributes.
Second method(s). If the differences are all or almost all within a small tolerance, run an Integrate. Or create a topology using feature classes, and run a validate. Priority is given to your Boundary layer.
Third method. Use the zipper task.
Fourth method. Use the construct features tool to first split all the BreedBlocks where they extend beyond Boundary, then delete those. Run it again building polygons taking into account existing polygons, and then merge these newly created polys (that fill in areas between BreedBlocks and Boundary) with the appropriate abutting poly.
