yes, different papers/broadcasters have different audiences so will choose different stories. Not just the lead but all stories. You get to choose which outlet you like best.
looks like tomorrow's papers mostly go for Corbyn. The Star and Sun lead with Jim Carrey's ex killing herself, the Mail has police chiefs saying they will turn a blind eye to people smoking in cars when it becomes illegal, the Express leads on back pain (must not be any McCann stories around), and the FT has the slump in global equities. All of which is pretty much what you'd expect.
just spent a week in Greece being rained on every day, ummmm... looks a lot nicer here. At times like this the weather forecast is more important than Isis and Corbyn.