Lovely home with wonderful potential! Of course, I assume you're planning to remove all of those over grown columnar evergreens? Not knowing where you live, I'd plant beautiful rhododendrons and azaleas (camellias too, perhaps) in a curvacious bed all along the walls. To make a Tudor statement you'll have to forgo having a storm door. I'm hoping you already have a chunky big Tudor style, stained wooden door.
Once you clear away those trees you can experiment with blocks of colors for your stucco, trim, and window casings. Like you, I prefer the more subtle color changes, like the other house, rather than the chocolate and white. I like the color of your bricks, however, if you do not you can put a diluted color wash on them.
If you know a skilled craftsman I'd consider to a little bit more Tudor trim decorations. There are plenty of pictures to see for inspiration. I'm not suggesting to go hog-wild and do something out of Chester, England, but I don't see any curves on your trim, and the ones on the other house you like has some. Enjoy your project!

I just remembered that I was going to suggest two large wrought iron sconces, and a large natural stone landing with the same stone on the walk leading to the street (cannot tell is I'm seeing a curb), and if money is no object (wheeee!), two square stone columns (about 3 ft high, or so to scale), topped with wrought iron lanterns.
Is that a small stained glass window to the left of your entry?

Thanks for the ideas. Yes, those cedars have to go! We live in a Zone 3 "Northern" climate near Edmonton, Alberta, so will have to pick up some hardy perennials or go with some smaller globe cedars. We had in mind to do a paving stone landing and curved walk. Natural stone would be nice but probably a lot more money? We live on an acreage (4 acres), so there is no "street", but I do like your idea of stone columnns with lanterns which our neighbours have actually done. Yes, that is a small stained glass window. Did you have an idea for that?

Most welcome! Depending upon the species you can grow rhodies in your zone, and maybe even azaleas providing they get the shelter they need; thank you Mr. Rothchild! : )
4 acres! Well now! That is a whole other gift to open! So how much land are we talking about in front of your home before reaching the public street, or does the size your estate make that not even an issue? When I suggested a large landing and a straight stone walk to the lighted stone columns I thought I was seeing a curb, and your house right on a public street. The rectangle and straight walk present a formal approach to a small front. No, but if you have a large expansive front then you could add curves to your hard-scape, which would, with curved beds all along the front, enhance the lack of architectural curves (and gables and high-pitched roof) that you love in the other house. If money is not object (wheeee...!), I'd raise the roof and use a strong architectural shingle that mimics slate. Barring that...
What you probably like about the other house is the stone facade around the front door; I love it! Consider adding one to break up the wall of brick around your front door. And that stained glass window? I'd keep it if it's period. The stone facade would enhance it. And any height you can give the roof over the front entry would improve it, but then again, the top of your home would be begging to be lifted to enhance the Tudor design.

More complimentary stone facade work on the corners of your home would work, too, as long as they make a strong statement, to few and too "wavy" is more of am English cottage look.