Having re-read the previous post, here are some obvious differences.
First here is a description of the Bohr model, which even refers to the Solar System.
This from googling "Bohr model of the atom".
In atomic physics, the Rutherford
–Bohr model or Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar
to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. (My italics).
Whilst some electrons may have slight difference (energy levels in different orbits) there is nothing like the enormous diversity of planets. vide
rocky planets to gas giants, cores, atmospheres (inc pressures), lack of solid surfaces, etceera.
One difference is that, above hydrogen, atoms contain protons and neutrons melded in the core. I know of no positive and negative stars (retaining identity) actually melded - not double stars.
There are, of course, planets orbiting double stars.
Another fundamental difference is that (IIRC) electrons are not regarded as individual spheres, but as 'spread out' through space.
Nevertheless, thanks for raising the issue - it always brings out some good discussion.