Ham sandwiches are disgusting. Unless it's from an actual honey baked ham or an honest-to-goodness Spanish ham (Jamon Iberico/Serrano, Italian prosciutto will do), it just doesn't sound appetizing to me. I'd say I find cold cuts in general to be disgusting. Unless I knew for certain that the cold cuts actually came from the pig/turkey/cow it's supposed to be impersonating and not that silly processed gunk with an Oscar Mayer label on it (or worse yet at Subway), I just wouldn't go near it... even at the local deli. Alright, pastrami is an exception, as long as I've seen it sliced from an actual side, but I digress.
French dips are great, as long as the meat itself isn't too dry. It doesn't matter how much au jus you drench in it, if the meat is chewy, well then that ruins it. Oh and BTW, the French dip didn't come from France and supposedly it was originated in L.A., at the famous Phillippe's dip downtown. It's called a French dip because of the French bread. Truth be told, you can't find or order a French dip in France.
That said, I'd take the ham sandwich, only by the way I'd prepare it, by the classical Catalan recipe I grew up liking. Take some rustic bread (a baguette will do), rub garlic and fresh tomatoes on the bread, a drizzle of olive oil, and authentic Spanish ham (Iberico, preferably). Breakfast of champions.