When taken in full context, I believe the answer becomes a little more clear.
"For we believe that Jesus died and rose again, and so we believe that God will bring with Jesus those who have fallen asleep in him. According to the Lord’s word, we tell you that we who are still alive, who are left until the coming of the Lord, will certainly not precede those who have fallen asleep. For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever." (1 Thes 4:14-17 NIV)
This states that those who are still alive will be caught up TOGETHER with those who died to meet the Lord. A simple way of putting the first part is that those that are still alive don't get a head start. The dead get to rise from the ground first. Then we're all gathered up in the clouds. God wants to meet all of us at once. No favorites.
"I declare to you, brothers and sisters, that flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable. Listen, I tell you a mystery: We will not all sleep, but we will all be changed— in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed. For the perishable must clothe itself with the imperishable, and the mortal with immortality. When the perishable has been clothed with the imperishable, and the mortal with immortality, then the saying that is written will come true: 'Death has been swallowed up in victory.'” (1 Cor 15:50-54 NIV)
As for this passage, it is speaking of how we shall give up our earthly flesh for new eternal bodies. We'll all be instantaneously changed "in the twinkling of an eye". The dead will raise from the ground in their new bodies and those that are living will be changed instantly.
So putting the two together, in context, says that the change will happen followed by us all ascending to be with the Lord together.