The Galaxy is about the biggest ship we've seen in Starfleet, at least on the non Abrams timeline. Thus, I tend to think of it as being rather whale-like in terms of agility.
"Agility" is really a fairly meaningless term in and of itself. In real sublight space combat it would come down to acceleration, and how fast that acceleration could be vectored in another direction.
In Trek, though, half the time sublight seems to be a matter of "Half impulse, helmsman!" and then a second or two later you're doing that speed. Then some of the time they order impulse in Spacedock, which should make Spacedock simply appear to vanish from around them instantly as the ship goes screaming out at 150,000,000 mph, and instead it just kind of drifts out at about 75 mph.
And once going, a Starship banks and turns much like a ship or aircraft does. Yet we never see a ship like the E-D pulling the kind of "crazy bob and weave" types of maneuver that something like the Defiant does.
Then you have warp drive, where we've seen everything from ships turning in a few times their own length at warp speed, through to canonincal statements that you can only go in straight lines at warp.
As with most things in Trek there's really no solid consistent canon of how ships maneuver to use as a comparison. So the agility rating is really just meant to give a "feel" of how well you'd expect one ship to maneuver against another at both impulse and warp. The Enterprise-D, to me, seems to be a big ship that's going to be not terribly maneuverable even though it can go at high speeds. It's sort of like Concorde, super-fast once it gets going but at the same time no fighter.
For an older ship with high agility, the feel I was going for was along the lines of putting a Sopwith Camel up against an F16. A Camel can turn on a dime in comparison, it's by far the more agile of the two in that sense... but it's never going to pose any kind of a threat because compared to the F16 it's essentially a stationary target, and being able to turn on a dime doesn't do a damn thing for you under those circumstances.
This is also an example of one of those places where the system really doesn't work too well - it's pretty decent for ships that are a reasonably close match for one another, like say a Miranda vs an Excelsior or a Galaxy vs Vor'Cha, but when a ship scores quite highly in one or two areas very low in every other, you're left with a significant overall strength when you really shouldn't. So for example you can generate a strength number for an unarmed ship on the basis that it still has speed, agility, shields, etc... which would mean, in theory, that a few dozen of your unarmed ships can defeat an armed one. Which is silly.
We sat down once and spent about a month trying to work out a system to cover these kinds of eventualities - one option considered was that the different factors should multiply, so that scoring zero in any one lowered the overall strength to zero. But whilst some systems worked better in some ways, every one we tried just ended up throwing up its own issues. In the end we decided to just go with what's there now as being about the best compromise we could manage.
Give a man a fire, and you keep him warm for a day. SET a man on fire, and you will keep him warm for the rest of his life...