You might think about using an inexpensive slate tile that coordinates with the silvery (or your stain) color of new concrete to add an accent of the area. What do you plan for your covered area? Dining? Seating area?

I found a couple of DIY videos and other how to's by Googling "install tile over concrete patio"

This is on my list too. We have a cracking and stained patio that we'd like to beautify. What about the deck and patio paints for an even easier and less expensive alternative?

We are actually spending a good amount of money to "beautify" the existing patio cover...T&G Beadboard ceiling, recessed lighting, etc. So the patio area will definitely have an outdoor dining theme. We have a separate area for fire pit / lounge area.

I'm just concerned that a standard pattern Slate (a standard tile with some color variation) won't look like it belongs. I've been trying to find examples here on houzz as well as other places online, but it seems like most people do one cohesive piece of either concrete stamping or all tile. I haven't seen any examples of a patio with tile surrounded by concrete.

Would staining the concrete be an option?

I think it's going to be hard to get a good answer when we can't really see what you have with such grainy and poorly lit pictures. Can you use a different camera a post better ones? You might also stand farther out in the yard, showing the new patio space with the old patio in the background. You mention that the patio is raised, but this cannot be seen in the picture. You need to show it so we can understand how it might have an impact, if it does.

Also, what would make a difference is your plan. Do you have one that you can post so we can see the layout. If the white line is half-way accurate, I can't imagine that the end result is going to look good no matter what kind of surface or finish you use. It's too contra for me anyway.