For me, the biggest difference is that, while Levemir and Lantus provide a reasonably flat response (one issues with the allegedly-non-existent "peaks" are resolved), MY basal needs tend to be quite curvy. I was never able to find a good balance on either Levemir or Lantus where my BG remained stables, say on basal testing -- usually, I have two big drops during a 24-hr period (for me, 4am and 5pm), no matter how I tried adjusting doses. Unless, of course, I was taking too little basal insulin for me needs the rest of the day...)
So, for me, MDI meant that I had to eat something to avoid -- or correct -- hypo events twice a day. I have no such issue when using a pump -- which was the reason I went to a pump in the first place!