There are 3 main differences between Pokemon Sword and Pokemon Shield
Note: Potential SPOILERS
Gyms: There are 2 gyms that change its type and Gym Leader, depending on which game. In Pokemon Sword, Bea is the Fighting type gym leader in Stow-On-Side, and Gordie is the Rock Type gym leader in Circhester. In Pokemon Shield, Allister is the Ghost type gym leader in Stow-On-Side, and Melony is the Ice Type gym leader in Circhester.
Legendary Exclusives: In Pokemon Sword, you can catch the legendary Pokemon Zacian, while in Pokemon Shield, you can catch the legendary Pokemon Zamazenta. Zacian is Fairy / Steel, while Zamazenta is Fighting/Steel.
Non-legendary Exclusives: Each game has its own set of exclusive Pokemon. For example, you can get Galarian Darumaka and Galarian Farfetch'd in Pokemon Sword, and Galarian Ponyta and Galarian Corsola in Pokemon Shield.
If you want the Legendary Pokemon that beats the other one, go with Pokemon Sword.
If you want to trade with your friends and be able to complete your Pokedex(which is easily possible), grab Pokemon Shield. More people have Pokemon Sword than Pokemon Shield, and as a result, are missing out on Shield exclusives. You are more likely to find someone with a Sword exclusive Pokemon that you need than a Shield- exclusive Pokemon.