What is the profit margin on each product at those prices? Knowing that will help determine which course of action to take.
If the slider is just as profitable (in terms of margin based on cost) then there's not much harm done in keeping them on the menu unless you can be certain that by offering two sizes that people are flocking to the smaller one when they otherwise would have probably bought the full size if they didn't have a choice.
The problem is that it's hypothetical until you test it. It's true, you can make the argument that your wife has and you're reducing the total number of dollars made if people opt for the small when they otherwise would have paid for the big. At the same time you can make your argument that says if you only have the one large sandwich, people may pass altogether, resulting in no sale at all.
But like you pointed out, you aren't keeping track right now, so it's hard to stay who is right. So I'd start by looking at how profitable each item is and go from there. If the slider has a much smaller margin, then it might make sense to drop it and focus on the one sandwich. Or maybe the slider has higher margins, which could offset the possibility that a few people are choosing that over the full size.