I would start with art..good art, larger chandelier and an area rug

Art in both places and more interesting chandelier hung a bit lower in the DR and maybe 2 floor lamps beside the sofa since the lamps I see are way too low .

^^^ what BeverlyFLADeziner said

In addition to the other recommendations, I think you could use some softness -- drapery in the dining room, a larger rug in the sofa room. Pretty spaces!

It looks like dining room got the better of the two rooms. Could you put the dining table into the living room alcove?

Another suggestion: the wainscoting trim is over the top. Consider painting over it with the wall color in both rooms. You still will see the design.

What are the gold balls on either side of the sofa?

A plant instead of flowers on the table.

Area rugs with more color (and a touch of that stunning blue) will perk up both spaces. Plus everything that Beverly said!

These are golden lamps beside the sofa both sides

Just thinking of some lighting ideas

Show the other spaces , please, and the kitchen beyond the dining, along with a view from living area into the dining room?

How about adding some artworks on your wall with some customized frames. I think it adds more life to it. You can check this out for more suggestions