In my tests the performance difference between "Classic" (v2) and Studio was only ~15% and that was in "Best Case" Scenarios...
More often than not they're indistinguishable in terms of performance.
Studio offers a little more "Refined" support for some ideas added to AppGameKit v2., such-as Enhanced Arrays and References.
Perhaps there is a bigger performance uplift on Mobile Devices (I don't know, as I don't really care much about Mobile Development; and the limitation of not supporting 3rd Party Plug-Ins in Tier 1 is a deal-breaker for supporting said platforms)
This said in regards to how much faster Tier 1 (AGK Script) Vs Tier 2 (C++ SDK) ... well it depends on how complex your application is.
In general terms (without threading) the performance metrics are roughly:
3.6 Million Ops / Sec - AppGameKit Script
2.6 Billion Ops / Sec - DBP BASIC
6.5 Billion Ops / Sec - C++ (Non-Threaded)
This said in terms of the Engine itself., eh... it is and isn't faster.
Like it is a bit faster as C++ Calls are quicker to the Engine with little overhead; but it isn't as the Commands still take a similar execution time (which is SLOW)
Meaning in most Scenarios outside of a much more Complex game you're going to be seeing a similar Framerate.
For me it Maxes out ~2,800 @ 2160p with a Basic Spinning Cube., where-as Cauldron (AMD's Open Source Engine Framerate) will hit close to 7,000 FPS., which is ~2x Performance; and the performance differentially will typically expand from there as you get ever more complex with what you want to do.
C++ (Tier 2) will out-perform AppGameKit Script (Tier 1) in Logic., by a substantial margin.
Where-as when it comes to the built-in Commands, it's only once you get a certain amount of Complexity that you'll see much difference; even then you end up limited by the Engine.
The lack of Threading, and focus on OpenGL / Vulkan Interop over taking advantage of Vulkan' more advanced nature; is what firmly limit AppGameKit both Script and Engine in regards to performance; and I continue to find this odd, given the intended development platform is Mobile; where you typically have far less Processor and Graphics power at your disposal.
In that situation outside of VERY small / simple projects; you somewhat HAVE to use Tier 2 just to get reasonable performance.