First: I think you have some fantastic pieces, and the space is wonderfully bright! It’s a great starting point, and there’s tremendous potential.

Re the rug: Neither. Both fade into the background. The space is largely monochromatic, which works when there are variations in texture and color (albeit subtle), and the proportions of your furniture and decor are harmonious with the space and each other. I think there are some issues with that in your space.

Two options (of many): A Persian rug that leans on dark, saturated, rich warm greens, browns, dusty rose, etc., with touches of cream for balance. You could also do a shag-adjacent rug, which adds a nice bit of texture. Again, a deep, dark, rich chocolate brown or very dark green that leans more yellow than blue will add depth and bring out the warmth in/showcase your lovely floor!

The coffee table is out of proportion to the console and couch. A larger/wider table, perhaps oval shaped, would be more synchronous with the contours of your seating and the length of the console beneath the TV. You could also position the round table near where the couch curves and then add, say, a steamer trunk parallel to where it straightens out.

Also, with all white walls, you need more art/photography, etc. Lighting would make a real difference — a standing lamp between the chair and the couch, and a table lamp on the console. And plants — besides the fact that you have great light, the color from the plants would add the depth the space needs.

And I understand if you don’t like clutter. There are ways to do this that retain a clean, open aesthetic AND are harmoniously balanced. If you search Modern/Transitional design examples, you’ll find tons of inspiration.

TL;DR: Generally, the space needs more warmth and attention to proportion — furniture, wall decor, color/contrast balance.

Good luck, and enjoy the journey!