The main difference is the available pkmn in each game. The majority are in both games, but its the rare ones that can only be caught in Sword or Shield. For example, each pkmn on the cover can only be caught in their respective game. However, this can be remedied by looking out for other ppl that can trade with you for the ones you are missing.
Another minor difference is bits of the story progression are slightly different, but ultimately, that doesn't matter in the whole experience of the game. The main story is fighting gym leaders to reach the final league. Each game has a few different gyms (2 or 3 out of the total 8).
Other than that, each game is basically the same - both solid pkmn games and fun to play.