But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth. Acts 1:8 KJV
And not only so, but we who have the first fruits of the Spirit, even we have sorrow in our minds, waiting for the time when we will take our place as sons, that is, the salvation of our bodies. Rom 8:23 BBE
The spirit upon endows us with power to do. The spirit within endows us with power to be.
The spirit upon is intended basically to endow with strength and ability for a specific assignment or ministry. We see examples with Judges, Kings and Prophets. However, the Spirit within is intended basically to conform us to the image of Christ. It is foundational. That is what identifies us as sons of God. It is a seal that we belong to God. (Eph 1:13, 4:30)
The Spirit upon in the new testament can be seen as the various ministry gifts (apostles, prophets, teachers, pastors, evangelists, care, administration, giving, intercession etc), gifts of the spirit (tongues, interpretation, prophesy, healing, miracles, faith, discernment, word of wisdom, word of knowledge) etc. As much as they are important, it is not the ultimate. They are important but as soon as their work is done, they are lifted. "Prophesies will cease..." 1 Cor 13:8. All these ministries are to prepare the body of Christ to become the habitation of God. "He gave... until we come to the measure of the fullness of the stature of Christ" Eph 4:11-13
However, the Spirit within is a more permanent expression. God designed us to be the temple of the Holy Spirit (1 Cor 3:16). He intends to make His dwelling among men. (Rev 21:3). While Paul encourages us to covet spiritual gifts (1Cor 14:1), He encourages us that love is the main thing (1Cor 13:1-13). Love is the platform upon which all gifts of the spirit are most efficient. Love is the most excellent way. We do not attain love by the 'Spirit Upon.' We attain love by the 'Spirit Within' (Rom 5:5). God is Love and God in us will help us become and manifest love-the main thing.
Both manifestations of the Holy Spirit aren't disjointed. As a matter of fact, while we fellowship together, the 'Spirit Upon' helps to edify and encourage others and also the entire body of Christ together. The gifts of the spirit as well as the ministry gifts are for edification (1 Cor 14:5). The word edify means to add brick to brick as in building up an edifice. So in essence, the purpose of the spirit upon is to create a perfect dwelling for the spirit within.
As we covert spiritual gifts, even more earnestly we should desire to be filled by the Holy Spirit. God will not restrain His spirit from those who ask genuinely. As a matter of fact, it is one prayer He longs to hear. If His will is to make His dwelling among men, asking for His spirit to dwell in our heart is foresight. It is like asking God to give us what He wants us to have. God's intention is for us to become and not to do. The most dreadful comment in scripture was directed at those who assumed doing could compensate for being. (Mat 7:21-23)
On a final note, I am personally convinced that the barrier between percieving the Holy Spirit as a 'thing' or 'person' largely depends on whether He dwells within or upon. Let me put that in another way: we fall into the delusion that the Holy spirit is not a 'person' because He doesn't live within. If all we have from Him is his anointing for ministry, knowing the personality of the Holy Spirit becomes an abstract adventure. A number of people view Him only as a force or divine influence, now we know why. However, when He dwells within, without controversy and having being a witness of His life, we know without doubt that He is indeed the third person of the trinity.
As we journey towards destiny, may every deed, thought, word and intention be focused on further conforming us to the Sons of God, the image of Christ and the habitation of the Holy Spirit.