Power + Attitude = Performance
With the combination of a power setting and an attitude the A/C will achieve a specific performance, simple as that.
Keep in mind performance is judged by lateral, vertical and linear (airspeed) quantities and not just one individual parameter.
So changing just one variable in the above equation will affect the performance in more than just one parameter, if you want to adjust speed but want to keep ROD/ROC constant both attitude and power must be adjusted to get that performance not just one alone.
What dose this all mean? well both throttle and yoke can change air speed and vertical speed, keeping in mind that when used independently or uncoordinated there will be a secondary, possibly unwanted or opposite effect as described in many of the previous posts.
Whatever action comes first it is the combination that gives us our performance be it what we want or not.