Mostly in the little details, and the overall emotional feeling. Examples:

(It’s not a change since OS X 10.0, but....) Right from the beginning having the menu bar at the top was better than the NeXT per-window menu bars (there were legal reasons for the NeXTStep behavior, sure, but a menu at the top feels so Mac-ish to me, that that difference alone is huge). Much of the conventions for menu organization/structure and so on (and definitely conventions for keyboard shortcuts, for the overall keyboard layout, &c. &c.) is much more Mac-alike than NeXT-alike.

Hardware finally caught up with the software (and the software was optimized better for performance), so that the interface is as “snappy” as OS 9 used to be on then-current hardware. (Early OS X felt terribly sluggish by comparison.)

The mouse acceleration curve reverted to something much more like the classic Mac version (in 10.3 maybe?).

The menus at some point (10.1? 10.2?) returned to the proper behavior of allowing diagonal selection. The alternative is a fundamentally broken interface, and every time I use an operating system that does it wrong I want to stab the guy responsible.

Finally in 10.4, the corners of the screen properly activated the Apple/Spotlight menus (taking advantage of “Fitt’s Law”).

Drag & drop support improved and was properly widely adopted.

AppleScript support by first-party apps got much better.

Dialog boxes got better writing, including somewhat more consistent use of verb buttons.

Did ⌘. (command-period) work everywhere (anywhere?) for cancel in dialogs in early versions of OS X? I don’t remember.

OS X print dialogs still aren’t my favorite, but they’ve improved relative to 10.0 print dialogs, adopting some of the feel of earlier dialogs.

Save dialogs improved a lot since 10.0. I don’t think ⌘D properly went to the desktop in early OS X versions, but I’m not positive about that.

Places where (in NeXT tradition) early OS X used “inspectors”, for instance in the Get Info window, later OS X reverted to the better "classic" Mac OS behavior. (This happened in various first-party apps too, but I’m not thinking of examples off-hand; it’s been a while).

NeXT-ish UI elements like drawers have been gradually phased out, in favor of UI elements which seem more spiritually Mac-ish. Oh, and remember early OS X Cocoa tab view widgets? Wow, were those dumb. Little wonder they’re pretty much gone.

I think support for Mac file aliases was sorta crappy in early OS X versions, but I don’t remember the details.

Cocoa applications started properly dealing with references to files rather than to path locations, for things like re-opening saved files, etc. etc.; early versions of OS X were filled with apps which would behave improperly when a user moved a file.

Exposé feels much more like a culturally Mac-like feature than the use of the Dock, etc. Though Spaces seems more NeXT-ish to me (I don’t remember if NeXTStep had multiple desktops... did it?).

The appearance of OS chrome tended back towards the simplicity of classic Mac OS (obviously not to the precise appearance, but to the feel), with every OS version further away from pinstripes, distracting transparency, slow unnecessarily flashy animations, etc. And not only the overall window ornamentation. Take a look at the folder icons, for example, which look like OS 7.5 icons (I always hated the ones from OS 8–9).

The Finder never regained its spatial-ity (as John Siracusa periodically laments), but it got much better at remembering window state in each version from 10.0 to 10.3.

Disks get properly mounted on the desktop by default (I don’t remember precisely the history of this, but I believe the default was not to show them on the desktop at some point; maybe I’m just confusing early OS X with Windows here).

The Finder at some point (10.4? 10.5?) finally allowed icons to be spaced closer together as in "classic" Mac OS.

The Finder got back color labels in 10.3, an OS 7 feature, which I believe were missing altogether from 10.0–10.2.

Finder keyboard and mouse selection behavior, especially in list mode, improved dramatically from 10.0 to 10.4. In general, the mouse and keyboard behavior of list widgets – rows, disclosure triangles, heading sorting and column resizing, etc. – improved quite a bit.

* * *

I’m sure there are dozens of other such things (if you read through Siracusa reviews and John Gruber’s notes about each OS version I’m sure you’ll find a bundle), but listing more here doesn’t accomplish much. I’m not trying to argue that "classic" Mac OS feels the same as the current OS X does, or that OS X doesn’t also include many very NeXT-feely features like the Finder column view, &c. I do think though that OS X is somewhere between a NeXTStep/Mac hybrid and its own thing altogether, both in specific features and in less tangible “how it feels” aspects.