Which lets more light in?

I need some help technical help please. A fan on my FB page is asking me some questions about taking photos of the northern lights. I have explained my equipment, settings, etc. however I'm far from an expert.

She is shooting with an older crop sensor camera. she tried some photos with a 50mm 1.4 and they didn't turn out well. She was shooting at 800ISO and said she gets too much noise at 1600.

I discussed the limitations of a 50mm lens on a crop sensor when it comes to star trails (only allows about 6 or 7 seconds before getting trails) she also as a kit 18-55 thats f3.5 at 18mm.

So here is where i'm confused. Which way should she go to get the most light onto her sensor? With the 18mm she should be able to to take about an 18 second exposure at 3.5 vs. a 7 second at 1.4.If you can answer this, I would love an explanation on how you come to your conclusion. Thanks.

If you are asking which combination provides more exposure the 7 seconds @ f/1.4 is roughly 1 1/3 stops more exposure than the 18 seconds at f/3.5, because there are 2 2/3 stops between f/1.4 and f/3.5 whereas there is only (roughly) 1 1/3 stops between 7 seconds and 18 seconds.

An easy way to compare combinations is an Exposure Value table or calculator. My calc shows a difference of 1.3 stops

F/3.5 to f/1.4 is a gain of 2-2/3 stops. 18 seconds to 7 seconds is losing ~1-1/3. Subtract the latter from the former and you're left with a gain of 1-1/3 stops.