This is a challenging question, but I note I have less knowledge of Gray's ideas than I do Higgins. That said, here's what I seem to gather from contrasting these two theories.

Gray's theory is focused predominantly on behavioral learning as it relates to a biophysical system. In contrast, Higgins' theory is centered more around goals and personality (if one frames personality in terms of attitudes, beliefs, value systems, etc.). From Gray's perspective, motivation is tied to a reward/punishment belief system such that promotion is consistently tied to reward where as inhibition is tied to punishment. Higgins' ideas contrast with this. To Higgins, promotion motivation can be linked to either a reward - or - a punishment outcome, and likewise prevention motivation can be linked to either reward - or - punishment.

The reason for this difference with Higgins is that people have different ways of perceiving their actions relative to goals. As an example, consider two different soldiers in command of a unit in battle. Leader A is promotion oriented. This leader will seek ways to advance her unit in battle to gain a new objective. If this leader adopts a prevention orientation (i.e., perceives failure in the advance), then she will experience anxiety. The anxiety will arise from a disconnect between her motivation to promote a gain versus perception of loss.

Alternately, consider Leader B who is prevention oriented. This leader will seek ways to protect his troops, avoid casualties, and avoid losing already held objectives. If this leader shifts focus to advance and attempt to gain, Higgins' theory predicts that the leader may not make optimal decisions because of losing sight of potential loss or danger. Effectively, the leader will act over-confidently, jeopardizing the unit.

So, from what I see, the effective difference is that Gray's theory is more absolute - promotion is linked to positive outcomes whereas prevention/inhibition is linked to negative outcomes. Higgins, in contrast, permits a more flexible system. Whether promotion or prevention yields a positive outcome depends entirely on the individual's cognitive style.

As a final thought, I suspect these two theories work in different domains. To me, Gray's ideas are best understood in terms of biological activity and basic behavioral learning whereas Higgins' ideas are better framed under personality, goals, motivation, and higher-level decision making as related to cognitive fit (cf. Affect as Information theory and Action Identification theory).

I hope this helps and look forward to anyone else's perspectives, comments, and/or critiques!

For someone who says that they don't have allot of knowledge about Gray's theory ... Jay Michaels does a fantastic job.

To sum up: Gray has a match between promotion/reward and prevention/punishment, and Gray's theory is really about behavioral learning. Higgins is really about cognitive framing, and there need not be a match between promotion/reward and prevention/punishment. 

The above is a really short summary, but I think it works well. 

Some research has demonstrated that performance improves on goal type tasks when there is a match between promotion/reward and prevention/punishment. This makes sense and seems to allow for better fit with lower level theories like that of Gray. That said, Higgins theory has also been used on "lower" level tasks (well lower than things like goals, or complex decision making) like categorization. The main authors of those categorization articles are Maddox and Markman. 

See, for example,

Maddox, W. T., Baldwin, G. C., & Markman, A. B. (2006). A test of the regulatory fit hypothesis in perceptual classification learning. Memory & Cognition, 34(7), 1377-1397.

Maddox, W. T., Baldwin, G. C., & Markman, A. B. (2006). A test of the regulatory fit hypothesis in perceptual classification learning. Memory & Cognition, 34(7), 1377-1397.

Grimm, L. R., Markman, A. B., Todd Maddox, W., & Baldwin, G. C. (2008). Differential effects of regulatory fit on category learning. Journal of Experimental Social Psychology, 44(3), 920-927.

Hi John - just wanted to comment with thanks for your providing some excellent citations. I've not read most of these articles but look forward to doing so. Thanks again!