pcjacobi is a Jacobi preconditioner (also known is point-Jacobi preconditioner). For this preconditioner, you just take the diagonal elements of the matrix and invert them for the future use in the iterative solver.
pcbjacobi would be a block-Jacobi preconditioner. For block-Jacobi, you don't take individual diagonal entries, but use small matrix blocks that are on the matrix diagonal. Now, you need to "invert them" whatever that means. A properly configured (block size) block-Jacobi preconditioner usually gives better convergence than point-Jacobi. However, preconditioning and iterative solvers are definitely connected to dark arts, thus you always can find some counter-examples.
Now, in your case, probably the matrix does not have any zero diagonal entries; thus point-Jacobi works fine. And the way you configure block-Jacobi results in preconditioner featuring non-invertible (or poorly invertible) blocks, leading to the preconditioning problems. I suggest you take a look at the PETSc example on block-Jacobi to identify your particular issue.
Regarding parallel processing: I would play more with your particular problem set, understand how different iterative solvers, preconditioners, and their parameters influence the convergence before evaluating the effect from parallelization. And ask it as a separate question later.