In general, a photo with distinct shapes separated by high contrast would look great as a black and white image. Both of the photos above work very well as B&W's because they contain distinct shapes of relatively high contrast.
The blue image (an LA Metro train station) has the dark perpendicular bars, while the architectural image (the full scale replica of the Parthenon in Nashville) has the darker long narrow ceiling that stands out from the lighter walls.
However, something else has to be considered. You must ask yourself, "How important is the color to the image?" You as the artist, the creator of the photo, must answer that yourself. Look at both images side by side and go with how you feel. Which version moves you more?
Regarding these photos, I prefer the blue image to it's B&W version because the color makes the photo. I love the blues too much to let them go!
The Parthenon photo could go either way for me. I like the sepia tone look of the original (although it's actually full color), but the B&W creates more simplified shapes.
Take a look at your photos and choose one or two to convert to B&W, then compare and notice how each image makes you feel.
If you want to have some fun taking B&W photos with your smartphone, look into my Smartphone Photo Classes.
If you're serious about getting into B&W art photography with your DSLR camera, I provide individual instruction and can customize a program just for you.