Rest assured, not all mixed print looks are loud and discordant. With a bit of know-how, these outfits are nothing short of chic.
If the print is the same on both pieces, color is your variable. Try reversing the shades in the pattern or picking up one or two colors from the busier print for the quieter one. Since duplication of the pattern keeps the look cohesive, you can try going a bit wider by choosing pieces in complementary or completely contrasting shades.
More advanced is pairing different prints. If cohesion is your goal, choose prints in the same color palette. Or, opt for a geometric print in black and white to act as your "neutral," and then go a bit wilder with your second piece.