In order to even begin a proper discusion of this topic, there are some basics that need to be understood and some other concepts that need to be squashed because they just make you sound like an idiot. (You being generally plural, not you specifically, OP.)
Firstly, what engines are we going to talk about? All engines? An "Ideal" engine? D-series? B? K? Ford SVO? BMW F1?
Secondly, let us dispense with the term "boost." It means jack all scientifically and only confuses several well defined scientific concepts that you should be learning in order to make heads and tails of what is actually going on in a turbocharged internal combustion reciprocating piston engine. Instead of "boost" we need to use terms like pressure (relative or absolute!) and CFM, as those two things are interelated but dependant on the size of the compressor of a turbocharger in use on the engine.
Thirdly, "high" and "low" compression are relative terms, and until someone states what the mid-point is, we are just being vague which further clouds discussion. Also, one has to consider the effects of the entire induction system and intake cycle in order to account for at least some of the factors pertaining to what is more commonly known as dynamic compression ratio, and much more specifically related to as Volumetric Efficiency (VE). For example, I think anything under 10:1 SCR (S being Static) is low. Some think that is way too high for any seriously boosted engine. I think anything lower in most cases is criminally insane.
Fourth, let us realize that almost all of this discussion is going to have to be theoretical. None of us have the money to build two engines almost identically or at the very least use two sets of custom pistons and a lot of dyno time in order to settle a lot of this in an engine format that we are familiar enough with to be satisfied with the results. The difficulty of this test is how to create a combustion chamber design that is easily manipulated into having vastly different compression ratios while still maintaining equivalent quench properties so that the effects of quench are not mistaken for the effects of combustion chamber volume in the same style of engine. To this end, I would propose actually using a Y8 head for experimentation. I dislike the ports, but, that is mostly irrelavent to our inquiries. (I just know someone is gonna say "hey, I thought you didn't like the Y8 head.") I think this head is ideal because it exhibits very good inherent quench, a compact, efficient combustion chamber, and will make a very good top side for our combustoin chamber. Having built in quench pads in a stock head also allows us to change the volume of the chamber very significantly while still maintaining very good, consistent quench pads on the pistons. Many would suggest using vitaras as a test base, but, if we were to conduct these tests scientifically, we would need a custom piston built to match the Vitara's quench pads with a much smaller dish, or possibly even a flat piston. It would be better, scientificly, to have two sets of custom, forged pistons made, from the same materials and with the same quench pad configurations. This would eliminate any material differences and possible effects of heat transfer and possible tuning differences based on non-consitent material and piston design. The pistons would be made to have a compression height equal to the deck, and a stock MLS headgasket would be used in both builds to ensure consistent quench distance, thus keeping squish very consistent. The rest of the engines would be blueprinted to the same speficications. Now, we'd have two engines build as similarly as possible with almost all characteristics of them being exactly the same except for the dish of the pistons, and, necessarily, the piston weight, though the weight would have an almost negligable effect on the results of testing. The engines would then be installed into an engine dyno, broken in and tuned using the same absolute pressure (very important as I will explain later) and same BSFC (if possible, and further explaination to follow). Tuning to the same PSI is almost correct, and tuning to the same AFR would cover up some very fundemental differences. Doing things this way at first would show us the characteristics of the combustion chamber itself, it's effect on how it spools the turboand how much power is made where in the working range of the engin. After this is done, each engine would then be tuned to it's own maximum potential, regardless of absolute pressure and BSFC, until the engine is destroyed. (I told you this would be expensive.) This should show the limit of the larger and small chambers and give us a very good idea of some general parameters that can be applied to "large chamber" builds and "small chamber" builds.
Issues with this test:
1. Cam. Finding a cam (or cams) that will provide a wide powerband (I would suggest from 2500-9000RPM) is difficult. I would suggest a Bisimoto 2.x or 3.x cam. I am sure Bisi would love to help out with something like this.
2. Turbo. Finding a turbo that can stretch the limits of a custom build and yet still spool earlier enough to help determine the effects of compression on spooling a turbo.
3. Manifold. There aren't many manifolds on the market that I particularly like. I would suggest having Bisi design a custom piece and then having two made. Bisi and John at Hytech are the only two people I know of that could handle that kind of thing. I would rather not have to run into a manifold limiting the engines, and I certainly don't know enough to design something like that.
My suppositions based on what I have researched:
The "small chamber" engine will produce more power everywhere, spool the turbo faster, and accelerate faster than the large chamber head, up to a point where the chamber reaches maximum capacity, and cannot be filled anymore, providing an actual limit to how much A/F mix can be burned, and therefore imposing a power limit for whatever fuel is chosen for the test. Various fuels could be used in the test before the final maximum power tests in order to find a fuel that would best showcase the chamber. (I don't care what fuel it is, and would take some testing. Or we could choose something commonly available and go with that as a standard, but then we might run into an octane limit, not a chamber limit. Even though the chambers will have very good quench, pump gas may not actually allow for a full testing of the chambers' limits.)
Once the small chamber's physical limits are reach, so that no matter how much the pressure is turned up, the engine won't fit any more air/fuel, the large chamber will start to shine. It will be able to engulf more mix, and thus, make more power. However, the difference in chamber volume will make it accelerate slower at lower RPMs and higher towards the end of the engine's working range.
It is also my belief that the smaller chamber will "work better" on pump fuels, meaning that the engine will accelerate faster at all RPMs as the engine will produce much more average torque and will require less time to fill the engine. Also, I predict that the smaller chamber engine will exhibit lower BSFC, meaning it will be overall more efficient. This will be better for any kind of car driven on the street. (My opinion.)
The larger chamber engine will most certainly be better for drag racing and highway pulls. It will be less efficient, and not accelerate as well until later in the engine's working range.
Then we can further complicate things like trying to pair a large chamber engine with a smaller turbo, a small chamber engine with a larger turbo, etc. But, we don't have the money to do any of this stuff, so, IONO. It's fun to think about and discuss, but hard to determine.