It's not really about whether the effects themselves are superior. Rather, it's about the much greater range of tools for animating properties of those effects, isolating portions of layers for effects, and compositing. In these regards, After Effects is far superior to Premiere Pro. On the flip side, Premiere Pro is much faster.
So, if you just need to do a quick color correction to an entire image, Premiere Pro would be better---but if you need to isolate faces for secondary color correction, After Effects would probably be better.
To give you the idea, here are a couple of movies that show a couple of different ways to selectively apply effects to a region:
Fixing the color in a single element is probably easiest with Colorista. I think it's hands down the best color correction / color grading plug-in available for the money.
There's a free version that could be used in PPro or AE. In AE I'd apply it to an adjustment layer with a mask tracked to the object. It all depends on your shot though. I see that you're trying to fix an interview. A screen shot would help, but I'd probably use AE.
You could also use any of AE's other color correction tools on an adjustment layer or on a duplicate layer with a mask. Hope this helps.
I really appreciate the link to the free Colorista. I didn't know they had a free version. I'm looking forward to trying it, hopefully later today.
In the meantime, you were very gracious in asking for a screen shot. I'm giving you two, both raw footage shot on an Panasonic HVX-200p at 720p60. The first is what I'd consider shot with good lighting and the second, well, speaks for itself.
As you noted, this is an interview destined for a DVD curriculum (not a movie). I have to chroma key a background in AE anyway, so I was thinking that AE would be the best place to do this. Todd seemed to suggest in this thread that the AE & PP color correction tools are identical or at least work identically (the settings are the same), and that PP was in fact better for "quick color correction to an entire image", which is what I am looking to do since the whole thing was shot poorly with the key light too far away. I did do a quick test in AE using AutoColor and adjusted the White Clip down to .05% and got a pretty good result except that the inner eye sockets still looked very dark. Colorista may change the discussion entirely, however.
I deeply appreciate your willingess to help so actively.
Update: Just tried Colorista Free. The Highlight Control alone worked wonders. Looking forward to learning how to use it more. A very superior product.
Highlight adjusted only in Colorista Free, applied directly to the clip: