Don't close either. It may be useful to include a link in each in a blurb that goes something like, "my question is similar to this other one (add link here), but is about (differences) instead." That would also take care of any copycat or plagiarism concerns. 

If they're similar questions, but not duplicates, then that means they're different questions which will garner different answers. And at the end of the day, they're both accomplishing what SE is here for, they're making this a place where you can get your questions answered.