Out of curiosity, I wonder what the pattern is for the Church of God in Christ, the “black” version of the Assemblies of God, formed at the beginning of the Pentecostal movement just like the AG, but during the time of segregation.
I was writing my post as you asked this, see my earlier comment on some of the CoG differences. Fundamentally, both are pretty similar in what they believe. In terms of how each denomination expresses outreach, AG focuses a lot on overseas missions, while Church of God works more with the local community. In that way, Church of God is larger than the AG in the US, but worldwide AG is huge.
I don’t think any merger would happen anytime soon, but the relationship between both denominations has improved significantly.