What comes to my mind is that the Trinitarian formula brings a deeper sense and meaning to whatever we do. Be it in prayer, deeds, talks. Doing everything in the name of the Father, Son and Holy Spirit is inclusive of the entire gospel and all the God has revealed, which in the end include Jesus name as well.
Doing the same things through life in only Jesus name can be exclusive of what the gospel is really about. We see the revelation of the Trinity, love of God the Father. A constant work of the Holy Spirit in Jesus life.
Both "formulas" are mentioned in scripture because I think they target matters in different situations and from different perspectives. Matthew 28:19, the command has a very different vision and universality attached to a different topic, namely baptism.
While in acts 4: 12 we read concrete about salvation, and through which name that is given.
"And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved.”
There is, as always, need for the One True Church to guide us into the balance of both formulas. Misuse of "In Jesus name" has as mentioned before, lead to heresies and people questioning his relation to the Father and the Holy Spirit.
Pray for me and forgive me, the sinner.