What are the exact differences between the refit USS Enterprise and the USS Enterprise-A?

Both the refit and the A variant are considered Constitution Class Starships. Externally they are identical, while the majority of internal differences are cosmetic or layout in nature. The torpedo room is more automated in the A compared to the refit, with smaller but equally strong torpedoes. But otherwise, both had the same speed, offense and defense specs.

Athough both ships are classified as "Constitution" class, there are several differences between the two. The original NCC-1701 was an older-style Constitution that was upgraded with more advanced components, whereas the NCC-1701-A was a brand-new, state-of-the-art vessel as of its launch. The two vessels appeared identical externally, and the dimensions and layout of both vessels matched up as well. Internally, however, was a different matter altogether.

The NCC-1701-A had numerous improvements over its refit predecessor:

• Enlarged bridge
• Automated systems
• Separate shuttle bays
• Vertical warp core
• Enhanced security features
• More advanced brig
• Early replicator technology
• Full-height jeffries tubes
• Officer's dining hall

Many of the improvements were from an aesthetics or usability perspective. However, the majority of systems became automated on the NCC-1701-A, which could conceivably offer an advantage (perhaps a decrease in reaction time) during combat.

There was one external difference. They had to repaint the model so the pearl accents on the engine section were originally a greenish-grey on NCC-1701 vs a light blueish-grey on NCC-1701-A. It's subtle, but for a bit of fun one can assume that other Constitution class refits might have had slight color differences: maybe a violet-greyish for some, or maybe reddish-grey?

There are some differnces externally, windows and paint job.

This is a possible addition to most of the answers which have mostly covered the differences. It bears mentioning that in my opinion at least until The Undiscovered Country, it is my contention that the Original Refit Enterprise was superior in overall power, resilience, and some equipment to the Enterprise-A, assuming she had her full crew.

My points in support of that statement:

• The A is in horrific shape as of ST V, and even Scotty couldn't get her fully functional by that time. In fact, he didn't refit her in the first place, and likely the engineering team that did was of undoubtedly lower skill than he. Whereas just prior to ST I, Scotty had refit the original Enterprise himself.

• Expanding on the first point Scotty put a lot more love and work into his favorite ship, the original, and likely she had advancements in all of her systems beyond what you would find in practically any other ship at the time. He also very likely kept these updates current all the way up to even ST II. This made it unlikely that the A which would have been just an "average" refit would be able to edge out the original Enterprise in anything but convenience and automation. I.E. the "old age" paraphrased by the Commander of Starfleet in III likely refers to the combination of spaceframe age, and her current battle damage. It was probably his intention to give a superior crew a more advanced ship, possibly the next production line Excelsior class made. (Script needs nonwithstanding)

• While it is just conjecture, and/or changing of the times in movie making, the Original Refit Enterprise defenses in most cases seemed superior to the A as far as on screen battles and shield strikes were shown. The original held together longer, and seemed overall better equipped for her missions altogether, again likely due to Scotty and his teams putting in that extra mile with her.

• Though rare across episodes, super advanced Aliens still had done some modifications to the original ship, which might have carried over to the refit. This would give it an edge over the A in a variety of situations looking at it logically.

Well that's likely it, and while it is my opinions of course, I like to think that it warrants mentioning the above in this discussion. Lastly, I also like the coloring of the Refit better I.E. in ST II, in almost every way, and I like the ST I bridge best to go with it. So I think the original Refit wins there too.

Let me know what everyone thinks.
(I would have preferred to have just left a comment, but insufficient reputation so..)