The seating die is much larger in diameter to accommodate the bell you put on the case in the charging die to help a cast or swayed lead bullet enter the case mouth cleanly.

If you are having issues with the case not wanting to enter the seating due, it either has way too much bell that is hanging up on the die, or you don’t have enough and the bullet is hanging up on the top of the case.

I’ve loaded well north of 30,000 rounds of .38 Special and .357 Magnum with at three different non Dillion die brands (RCBS, Lee and Lyman) and never had an issue, provided you set the charging die to put a correct amount of bell in the case mouth.

If you consider other cartridges, I’ve also used CH, Redding, and Pacific dies as well as Dillon.

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I have similarly never had issues with non Dillon sizing dies.

However, the paperclip looking spring arm on the case feed plate can cause problems if it is not properly adjusted - especially with long straight wall pistol cases like the .357 Mag. If the end of that spring arm is too high and presses on the case above the level of the shell plate, or os adjusted too far in so that it rides up on the case, it will push the case mouth in toward the center of the press and it will hang up on the edge of the sizing die.

Conversely if it is not adjusted in far enough to just be just barely short of to just barely contacting the case it won’t hole the case against the inner edge of the shell plate and the case mouth can hang up on the edge of the sizing die.

It can be deceptive as the same adjustment works for a whole lot of different cartridges - right up until it doesn’t, and that can cause people to start blaming the seating or sizing die when those are not the problem at all.