If bringing both running shoes and dress shoes, it would probably be better to wear the running shoes and pack the dress shoes.

1. Running shoes are often bulkier, so wearing them and packing the dress shoes may leave more room in the luggage for other things.

2. If your dress shoes are uncomfortable, you won't want to walk around airports etc. in them and wear them in the plane.

3. If you have to run to your connection, you'll do it better in running shoes than dress shoes.