I prefer the Lee way, theoretically. In practice, all my Lee-installed gas checks are straight, and I don't see how they could be any straighter. But I'm sure lubesizers also work just fine.
Now, my reasoning could be total crap. But here it is.
With a lubesizer, the bullet goes in base first. As the oversize check is first to enter the narrowed part of the die, there's no guarantee it doesn't tip as it enters. Imagine trying to push a quarter into a tube that is slightly smaller in diameter than the quarter. It will want to tip and go through sideways. That's the easiest path. The gas check has the same problem, and it's supported only from behind, by the base of the bullet. The gas check could potentially tilt away from the bullet on one side while it is being forced thru the sizer. Then when you mash the bullet all the way to the bottom, it gets partially straightened out when it finally hits the flat referencing surface of the bottom of the die. But it's already been sized by that point.
And even if this doesn't occur in practice, you should still preferably have the check on there squarely, BEFORE you put it in the lubesizer.
With the Lee die, the gas check is smashed between the flat seating stem and the base of the bullet. It's self-squaring. The check is supported front and back. Since the check reaches the sizing die last, it's going to be held nice and flat and concentric before and during the sizing process. It's being sandwiched between the bullet and seating stem by maybe a couple of dozen PSI throughout. So throw it on there any which way, and watch perfect checks come out the other end.
I know that you've had some bad experiences with the Lee sizers, and I wonder. Maybe you were installing checks on bullets that were already sized? The force of the bullet sizing is part of the self-squaring process.