I am going to have to give up some. I think their idea is a brillaint one. Also I really need some co-founders. I have been going at it by myself and we all know what PG things of that...
From what you describe, it would be better if you guys do a merger instead of run two different companies.
Do a merger and figure out the split based on what each of your cofounder brings to the table. This makes more sense if your business and theirs compliment each other and are both in the startup phase.
Right now I sense that you are confused about what exactly you want out of this. If you are looking for a cofounder, a merger makes much more sense than equity swap which doesn't get you a cofounder.
In most innocent sense it doesn't make sense why you would give up 40% for their 20%. Not that this means much without knowing any detail about what level each startup is in.
Ask yourself if their company is worth twice yours right now. You would know better.