Apple - How to access "Faster (fine)" and "Slower (fine)" playback controls on VLC for OS X? Else, what alternative?

Yes, VLC for OS X provides this level of control.

If you go into VLC » Preferences [aka. ⌘+,] » Hotkeys you'll find that you can associate hotkeys for both actions – Faster (Fine) and Slower (Fine) – and more:

You can find plenty of options here:

• set them up the way you were used to using them on Windows,
• set a hotkey for resetting playback speed back to normal etc.

Note: If your newly assigned hotkeys don't seem to be taken into account, you might need to quit VLC and start it again.

I just downloaded VLC 2.0.1, and in the Playback menu, it has a slider that allows for finer control (note when pressing command + =, popup text says playback speed 1.5x, but in that slider it shows 10x, which means that 2x, 3x, etc. in that slider would allow for finer control)

One of my favorite media players for Mac is Movist – I think it's much better, smoother, and faster than VLC.

Using the ShiftApple← and ShiftApple→ keys you can adjust playback speeds in 0.1x increments: 1x, 1.1x, 1.2x, etc.

And ShiftApple\ to instantly go back to 1x.

Note: the link above is for the open-source version, 0.6.8, which works great. There is a newer version 1.1.4 for $5 on the App Store as well.