Hello! I am the original developer of Learn Chess with Dr. Wolf 
Diamond membership is totally different from Learn Chess with Dr. Wolf.
Both have one week free trials, so you are welcome to try both and see for yourself what you like.
Having it all together some day would be great, of course — hopefully someday we will.
In the meantime — Diamond membership offers a very broad range of resources. If you haven't seen the feature description here you should check it out. Puzzles, puzzle rush, lesson, video lessons, retry mistakes, unlimited analysis, it's a big package.
What Dr. Wolf offers that you can't get anywhere else is real-time feedback on your moves while you play with Dr. Wolf. There's also a Training area where you can practice against tough positions from your own games. And I think Dr. Wolf's lessons are pretty great.
But really, different people will prefer one or the other for different reasons, they are quite different offerings. I hope you give both a try!
I'm starting to get into chess and want to kick it up a notch. I don't have unlimited resources, so if anyone has tried both, what would you recommend?
Apart from the video library, the diamond membership supposedly features some additional analysis features. Do they compare to the Dr. Wolf app in any way..?
Does anyone know if the analysis capabilities from the Dr. Wolf app will be incorporated into chess.com? I would love to have it all in one place/app, obviously.