I have only advised a few undergraduates on projects like this, although I participated in several undergraduate research projects including an REU and a baccalaureate thesis.

Working on open problems versus reading existing proofs is a false dichotomy. 

First, it is common to have students do both: Have them read through papers you select and work on a problem. 

Second, those aren't the only two options. There are many things that are not known that are not called open problems. A student can collect data testing a conjecture, and this can range in difficulty from a straightforward calculation or programming exercise to something requiring real ingenuity to check examples with intrinsic interest. A student can apply a result to a case of interest.

There are many questions mathematicians ask which are not universally called open problems because people haven't looked at them much. This happens at the ends of many papers, and many talks. The author of a paper might be saying, "I think the techniques used in this paper will work on the following problems but I don't have time to look at them." These are often much better problems for students to work on than problems that are known to be open because they have been shown to many people who have verified that the easy/standard techniques don't work. 

Part of mathematics is exposition. You can ask a student to rewrite a known result better, using different notation or filling in the details. When a result was a culmination of multiple papers, it might be that the overall exposition is very different from what it should be. Fixing that might be a good task for a student... or it could be far too hard, and a good task for a team of seasoned mathematicians, as in the case of the classification of finite simple groups. Many masters theses are improved expositions of known results. I have found a lot of nice expositions written as senior theses.

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Advising undergraduates properly can require a significant amount of preparation, and it should not be undertaken lightly. I think you should focus on the educational benefit to the students instead of the potential value of the research, so lean toward having the undergraduate read good papers and pick up useful ideas and skills over having the best chance to produce research. Further, the student is likely to run into obstacles and to be unable to produce new research within the short amount of time allowed. When that happens, will the student have something to write up anyway? Try to make a project with many ways for a satisfactory conclusion. It is easier (but not necessarily easy) to schedule progress through experimental calculations, reading, and expositions than it is to plan on research progress.