So with the recently revitalized rumors that John Constantine would be making an appearance on Arrow I thought it would be interesting to talk about what would happen and why it would make more sense if he appeared on The Flash.
As we all know CW's The Flash uses lots of science to explain all of the weird stuff that happens on the show, such as Meta Humans, and time travel. John Constantine is an exorcist so on his show he dealt with all things magical, and demonic. Because of the radically different themes of the shows if John Constantine showed up on the Flash the characters would be butting heads on the ideals of science vs. magic, which is always interesting.
If Constantine appeared on Arrow I have a feeling it would be very similar to the Arrow side of the Arrow/Flash crossover, but instead of just Oliver Queen dealing with his morality it would happen with Constantine as well, and I don't think anybody really wants to see both characters feeling bad about themselves because of their misfortunes. The other thing about Constantine appearing on Flash is that magic would go really nice with the multi-verse theme of season 2 of The Flash.