I think momo and Annop are right that the "run into" variant sounds less enthusiastic. :) If someone says "I hope to see you again" then that sounds unmistakably friendly. It's more or less an invitation to actually do something about setting up a future meeting some day. If someone says "I hope to run into you again" then that's less clear. That does not sound, to me, like an invitation to set up another meeting. It's about leaving it to chance whether they meet, but still hoping it happens, or at least claiming to hope it happens. The truth could be: "I would actually prefer not to run into you again", "I really don't care one way or the other", "It would be nice to run into you again, but not quite nice enough to bother setting something up", or even "I really like you and I really want to see you again but I'm going to say 'run into' in order to sound cool and hard-to-get."