Your question is a bit too vague. TrustZone by itself doesn't really give you anything. For instance, by default you run everything w/ TrustZone bit set unless you do something different during boot.
In general, I would say TrustZone is not special at all (yet) in regards to immunity to side-channel attacks. See: https://twitter.com/bryanbuckley/status/912458210191093760 On the other hand, TZ (NS bit) was a bit special for ARM so maybe they paid more attention to it (i.e. maybe it matters greatly that addresses are tagged NS/S for the HW, unlike x86 which was not designed to consider addresses part of securable boundary between modes/rings?). Or maybe ARM still opted for speed over security, in some surprising/disappointing ways.
However, that may be a moot point if you can execute arbitrary code in SWd and if something like Spectre might leak SWd usr to SWd usr (since you could then use normal communication between the SWd/NWd)?
Of course folks will experiment and we will know in the coming months.. if a TEE vendor does not first make a comment (e.g. linaro). Also remember that the TEE folks have different OSes (some are micro-kernels that are more security-focused).
Curiously, I saw the blog post in August last year and it reminded that it was during OMAP5 bring-up that I think I sent my first ever patch to lkml, dealing with aborts being spammed (being originated via speculation; aborting because we had a region of memory dedicated for TZ). A15 had introduced a deeper branch prediction buffer, iianm.
I can't find the final patch. Hopefully my sign-off was just omitted rather than the commit living in some OMAP specific fork. My RFC patch was pretty dumb (basically I disabled speculation during early linux loading, re-enabled once "the real" page tables were ready to activate) so better programmers took the helm and I confirmed the fix..
So anyway.. at least on OMAP the hardware _seemed_ to disallow any access at all across TZ boundary, even by hardware. Then again, you can't really trust this reporting/aborting (good sign at though) and would have to verify yourself w/ some PoC attack.
And obligatory mention that The Mill seems like a better CPU arch.
