The Mind Illuminated runs with the metaphor that using your mind is like sight. Attention is what’s directly in focus. Awareness is everything else in your peripherals.
Attention is serial highly detailed and concentrated. When you're so focused on a book or show or math problem that the outside world "doesn't exist". Flow.
Awareness is parallel, multi-directional distributed and about the relationships between things.
Attention can be split between things. This is called working memory. It’s the number of things you can hold in your mind at one time. roughly five or maybe seven? It's your mental whiteboard. A physical notepad gives you extra slots, making it easier to think. 
If your attention is the chef then your awareness is the surrounding restaurant. Waiters collect and schedule orders, apprentices prep ingredients. Awareness decides what is important and passes that to attention.
Our attention is one of the most valuable commodities. Carving out space to think allows you to face and make progress on problems. Extra attention has a compounding effect. Looking at the right things at the right level of granularity. Increasing the attention & awareness integration seems like a good thing.
Try: Your sight follows your attention. Try looking at this word. Without moving your eyes from the bold word become interested in your computer keyboard or something at the edge of your vision. You’ll find your eyes will want to move or they snap to looking at the keyboard.  That "becoming interested" thing is what I'm calling awareness.
 This is from Agenty Duck, damned if I know which post tho.
 Critch: Use a larger notebook to think better