I've been using Sublime Text 2 for Windows and Linux because it's simply the best for those platforms. However, when using OSX I have the option to use TextMake, which is where Sublime Text 2 seems to get its inspiration from.
Which editor works more seamlessly with OSX as far as speed, ease of use, OSX integration, and naturally intuitive keybindings?
Go with what you're familiar with and don't worry about whether you're missing something or not.
Familiarity will trump any additional features you might likely discover in TextMate and the ability to sit in a familiar coding environment no matter what OS you're working is a really big productivity boost.
Overall Sublime Text 2 is a move forward from TextMate at the time I'm writing this. It has better undo semantics. It can load in most TextMate bundles so you can extend it in the same ways TextMate can be extended. Though, truthfully, after switching from TextMate this year I haven't found a need to install any TextMate bundles because anything I had been using in TextMate was available as a better implemented, more feature rich bundle in native Sublime Text 2 format so far.
This being said, TextMate 2 is in alpha and can be downloaded, so an update is on the distant horizon. But my advice still stands: familiarity on multiple OSes is a fantastic thing for your development environment.
If you're using multiple platforms, then I'd suggest going with Sublime Text 2. Sure, some things just don't act natively on the Mac, but as Ian said, nothing beats familiarity.
Personally I've been (and still am) a huge fan of ST2. But recently I've switched over to a new application that is written in native Cocoa. It's called Chocolat. I've watched it get progressively more powerful through the betas, and It's definitely worth a look.
There’s no objective answer to this question. Both TextMate and Sublime Text 2 integrate very well with OS X and use intuitive keyboard shortcuts.
If you’re used to working with Sublime Text 2 on other platforms, it would make sense to use it on OS X as well.
I think TextMate 2 integrates better with OS X UX guidelines, it has a really beautiful interface, better finder integration and it has more Xcode-ish tools, like source control panels. Sublime Text does a pretty good job on integration, for a cross-platform software: it's interface's components don't feel alien in the system, it has support for overlay scrollbars, etc. In fact I think ST2/3 integrates better with OS X than with any other platform.
However, regarding editing capabilities I wouldn't stick with anything else than Sublime. It has better keybinding settings, it's way more extensible.
TextMate 2 is definitely an OS X app - along with other editors like Chocolat and Espresso - but if you're comfortable with Sublime, stick with it, it does a good job in order to not feel alien compared to the others.
It's not a direct answer to the question, but consider BBEdit. It's beautifully integrated with Mac OSX. It's fully modern, and has been rock-solid across 10 versions for 15 years (I've been using it for that period, since 1.0). A trial version is freely available; in addition, there's a freeware stripped-down version, TextWrangler.
