This shouldn't be happening, unless the big knife is pre-2008 and the little knife is post-2008.
Victorinox originally used a 2 MM red LED powered by a 3V lithium button battery (CR 1025). It is useful as a keyhole finder, and the red LED can be used in the dark without waking a sleeper. According to SAKwiki, "A White Light option, also using a 2mm LED, was introduced in 200x, and uses the same battery." I've never seen one, but I assume it had a similar dimness.
In 2008, Victorinox upgraded to a 3.5 MM white LED. It is more than twice as bright as the red LED, but it is not bright enough to reliably show footing in an unfamiliar place or over broken ground.
When powered by two 3V batteries, the 3.5 MM white LED shines 50% brighter and it becomes an adequate substitute for a AAA LED flashlight — not equally bright, but bright enough to save you from falling down a canyon or through a hole in the floor.
If your Spartan Lite has a 2 MM LED and your Signature Lite has a 3.5, the little knife should be brighter. If your Spartan Lite is the current production model, it has a defective LED light module.