Battle of the sliders! Little steamed cheeseburgers with onions! Mmmmmm.
Probably more an issue of “Which one did you grow up with?” or “Which one have you had?” but I’ll ask anyway, just for shits and giggles.
I had my first Krystal in Georgia about 2007. It was good, but it’s not a White Castle “slider” which is the “real” slider. 
To me a Krystal is close, it tastes like the White Castle hamburgers you buy in a box at a grocers
I’ve only had Krystal when on road trips, and it doesn’t compare to the White Castles I’ve grown up with. But I’m sure that’s just my personal conditioning.
My first exposure to Krystal was in the 50’s in Montgomery in what was then called an Aluminum Room. Seems they were a nickel each. They were a bit larger then and it didn’t take more than 5 to make the equivalent of a regular burger. I could usually eat 10 before giving up.
Nowadays we get them a few times a month and I go with 6 regulars. My wife gets the bacon-cheese version.
I have only had White Castle a few times, starting back in the 80’s.
WC has more of the fart ingredient, so I stick with Krystal. 
But they’re both gut bombs and that’s okay by me.
Link is funky but it gets close.