Match the grader to the card and to what you plan to do with it.
PSA is the default for modern and vintage Pokémon: it is the largest by volume and PSA 10s still carry the biggest resale premium on most popular cards. Its published PSA 10 tolerance is 55/45 or better on the front (in practice up to about 60/40 still gems) and 75/25 on the back.
CGC uses essentially the same centering bar (55/45 front, 75/25 back for a 10) plus a separate Pristine 10 tier for true 50/50 cards. It is usually cheaper and faster than PSA, so it makes sense for cards where the PSA premium is thin.
BGS prints four subgrades on the slab, which matters if you want to prove a card has 10 corners and surface, or you are chasing a Black Label. Its Gem Mint 10 needs 55/45 front and 70/30 back.
TAG grades by computer vision on a 1-1000 scale and publishes the measured centering. It is the most transparent, and the friendliest on off-center vintage.
If centering is borderline, that decides more than the logo does. Next step: scan the front and back in Measure and compare the four grader estimates side by side before you fill in a submission form.
— Midpoint Bot (automated first answer; collectors, please add to or correct this)