The way I approach the theological question is by looking at what types of things God’s Spirit is doing in the OT, and what the Holy Spirit is doing in the NT. I haven’t done looked at this for a long time, but based upon my memory and running through texts in both testaments in my mind at the moment, there are a lot of similarities – miracles, wisdom, faithfulness to Yahweh, being “caught up in the Spirit” and taken to new places (like Ezekiel and that guy in Acts – Peter? – after he led a man to Christ with Isaiah 53 and baptized him) etc. There are also differences. I think the differences can be divided into two categories (but remember I’m doing this off the top of my head).

One, in the OT, God’s Spirit rests upon particular people, often at particular times, whereas in the NT, particularly following Pentecost, the Spirit is received by the multitude of Christ’s followers as opposed to just a few leaders, and thus empowers Christians generally to do God’s work. I think this difference can be theologically understood from the perspective of the history of salvation – something really new happened historically in the relationship between God and humanity with the death and resurrection of Jesus, and this new form of the outpouring of God’s spirit is a consequence of that new thing.

Two, I think a category of differences exist on the level of certain activities, like I can’t think of a NT equivalent to all of Samson’s exploits, nor a NT equivalent to Saul’s “prophetic frenzy” (although I’m not sure the meaning of that is completely clear). But at the same time, I think the OT writers were often trying to say something like “this person was doing something we can explain in no other way than a divine spirit came upon them.” Which is actually still really similar to what I think the NT writers were trying to describe. I think it is reasonable to consider that God’s spirit leads to different particular activities in different times and places.

A further thing to consider when thinking about this question is that the NT authors were not speaking in a vacuum, nor were the Church Fathers (the ones who came to called “orthodox”) only looking at the NT when they formulated the doctrine of the Trinity – they were also drawing upon OT languages and images. Acts interprets and explains the events of Pentecost through the lens of Joel – so is it appropriate to say that “my Spirit” in Joel is different than the Holy Spirit we received at Pentecost?

I don’t mean to suggest that there should be a total theological leveling between the OT and the NT on the issue. The fact that our canon does DIVIDE them into two (imagine – Matthew could have been logically placed after Nehemiah in terms of genre) says that something fundamentally NEW did happen with Jesus and that human understanding of Yahweh would have to be radically reinterpreted in light of this new thing. But I am concerned that the academy has spent so much time over the past century learning to celebrate the DIFFERENCES, from an anthropological perspective, that I think we have lost a healthy balance with regard to theological similarities.