Should I replace a carport post as it was originally built or with an upgraded column?
The post looks reasonably adequate as it was originally built even by modern standards. If it wasn't you'd have seen disaster long ago, when it first started to decay.

To maintain the style detail I'd rebuild to match, using pressure-treated lumber. By doing so you eliminate the need to cut that notch and you end up with a more robust post. A single post member may have weaknesses that are addressed by using multiple boards. To be clear, each board should be cut accurately to fit its bearing points on each end. It's not just the center board carrying the roof load. 

I'd fit everything and screw it all together at 18" intervals with pairs of 3" corrosion-resistant deck screws from each side. After it dries out for a few weeks, use a high-quality wood filler to flatten out the screw heads, then prime and paint.