And I agree with "certain designers." Can you find a lower pile?

I would choose a rug similar in style to the turquoise one, with some of the same colors and/or tones, but a different design. But I'm saying this because you asked what I would put with the turquoise rug. Ideally I'd design the living room first and put the most time into choosing the right style and design of rug for the living room as a whole. Then I'd choose the rug for the foyer based on the living room choices.

Mmm yes perhaps a lower pile. I really dig that turquoise rug. Why not try for a lower pile rug in one of the lighter colors in the turquoise rug. I see a nice gold, taupe, or amber color coming out of there.

The two rugs are in rather different spaces and in different settings. The shag sounds fun for your eclectic living room. If anything, I'd keep that and switch out the smaller foyer rug; its size is less expensive to replace. Do turquoise again, considering the wall color of the living room, just less traditional.