In my opinion and experience, these apps help me WITH my old-school diet and exercise. They motivate me to move, allow me to more accurately track calories and make educated food choices. They give me graphs and feedback. The app itself isn't making me lose weight. It's motivating me to eat better and exercise more. THAT is what is helping me lose weight. Yes, I could do the same things without the apps (keep a paper food journal, track my exercises manually) but it's so nice for me to have MFP on my phone where I can look up calorie counts and add them no matter where I am. I love syncing my Fitbit app to see my latest steps and activity graph on the go. My Streaks calendar motivates me to work just a little harder so I can put an X on another day and provides me with a quick visual of how I've done this month compared to last month.
I'm sure there are many apps out there that do cost a little more upfront, or try to entice you with in-app purchases (I looked at the new Jillian Michaels app that has a monthly fee and passed on that myself. I know I'd do better with a basic video from her for a lot less). Just like any other health product, you have to weigh the pros and cons and decide you think it is worth the money. Even though this Yahoo article has the title Why Weight Loss Apps Are a Waste of Money the author seems to be siding with me on this one. This article What Weight Loss Apps are Missing was a little more insightful than the first three I stumbled upon.