compare two files by name ending, throw away one

Hi, maybe someone can point me in a direction to get this solved. I often get two picture-files which have the same name with a different ending
xyz_small
xyz_big
Since I sometimes just get the small (or just the big) file, i need a rule to compare: if the big one exists, then i want to throw the small one away.
Anyone with any help?
xyz_small
xyz_big
Since I sometimes just get the small (or just the big) file, i need a rule to compare: if the big one exists, then i want to throw the small one away.
Anyone with any help?