The all-natural beef patty (pictured left) is touted as being made of "grass-fed, free-range charbroiled beef with no added hormones, steroids, or antibiotics," while the regular beef patty (pictured right) is simply 100% beef. Both are charbroiled, as are all Carl's Jr.'s beef patties.
The Big Burger is the cheapest burger on the menu at $1.79 (and sometimes for a $1 promotional price) and includes a regular beef patty, dill pickles, onions, mustard, and ketchup on a sesame seed bun. Likewise, I got one of these plain with just the bun and burger.
The crust on both patties was dry, which suggests they weren't fresh off the grill but there was some moisture inside.
Overall, Carl's Jr.'s all-natural beef patty and regular beef patty were much the same with some slight difference. Depending on how much your local Carl's Jr. charges for the substitution, it might be worth it to get the all-natural beef patty for a little more meat and beefy flavor or if you're just into getting grass-fed, free range beef.