I can't really say the Atari 8-bit version of Galaxian is better than the arcade release, but it does pull off the impressive feat of being different while still being unmistakably Galaxian. Some players may even prefer it over the original.
The differences are mostly in the sound, and in the way the aliens attack when breaking formation. They move more quickly, with more complex patterns, and with more frequent changes in speed and direction. Of course the aliens could get pretty crafty in the arcade version as well, especially at the higher levels, but here the unexpected zags and sudden mid-air pauses start early, and only get more unpredictable as the game goes on. Fortunately the player's ship also moves faster, and enemy fire falls only straight down instead of at different angles. As for the sound, the new effects ironically seem less frantic than the arcade game's, and yet they still suit this game perfectly.
This release of Galaxian proves the Atari 8-bit computer line is more than capable of a faithful recreation of the arcade game, and yet the developers decided that wasn't what they wanted to do. Whether that's good or bad will have to be left up to each individual player. All I can definitively say is, it's different, but it's still Galaxian. That by itself is pretty remarkable.
(Note: The Atari 5200 and the Atari 8-bit computers have very similar hardware, and games were often published with the same code for both. Atari 5200 Galaxian has been tweaked to allow different speeds of the player's ship using the analog controls, but otherwise the two releases are identical.)