My opinion is that it will be tough to make two identical planters look the same with a significant difference in light. As you discovered last year, you will have one grow well and one less well, and which is better depends on what you planted. You can easily keep it similar (like red petunias in one vs. red impatiens in another) or if it were me, I'd mix up one or two same plants with different accent/thriller plants as the central focus.

For example, Bacopa grows nicely in either situation (still wont be identical though). With white blooms that cascade over, the idea would be to present the same color SCHEME (taller purples; shorter yellows, or what have you) vs. the exact same layout/plant. The eye would catch a flurry of your choice of colors on this side and the other -- without zooming into a noticeable size and quality difference of two identical plants where one is visibly thriving over to other.

Just my thoughts!

Thank you for the ideas. I used petunias, lobelia, bacopa, and white impatiens last year. Maybe if I try the same color impatiens and petunias, that will work better. The one plant that did well in both boxes was a spiky plant I added for height. Maybe I can add more green foliage plants and go for a general similarity of colors this year.

For foliage, I think both golden creeping jenny and heuchera would do well in both locations. There seem to be more varieties of heuchera every year. Some are more tolerant of heat and humidity than others. I've had great results with Caramel in full sun and part shade, though mine are in an east facing location. Limelight tended to scorch in full sun for me. All of the red and purple varieties I have seem to do well in sun, but I haven't tried them in a west facing location.