You have a lot of big questions here, so will try to answer them for you, but be ready for the diatribe of the century ;-) There is a simple rule when talking about power/torque output which goes: There is no replacement for displacement.
If you increase the size of the four cylinder (through whatever method) to match the size of the six cylinder, you will not usually have the same output. There is a rule of thumb which says, to get greater torque, you increase the displacement. To increase the horsepower, you make your engine spin higher. Torque gets you moving, horsepower keeps you moving. Even though the displacement of the four cylinder engine is same as the six cylinder, the six cylinder will fire two more times per engine cycle. This creates smoother power (less vibration). Think of using a huge single cylinder engine having the displacement as your six cylinder. While the single cylinder will be able to run, it will not spin up (rev) as fast as the six cylinder, nor will it be able to spin as high (rpm range) due to the mass of the single piston driving engine, as well as the mass having to be used to counteract the piston. To answer one of your questions, though, yes, you can usually increase the displacement of your four cylinder to match the six, but is it worth it? Hopefully some of what follows can explain what I mean.
There are two common ways to increase the displacement of any engine, by increasing bore and/or stroke. Some engines are a lot more susceptible to either of these modifications. I will use the GM Gen I Small Block Chevy (SBC) as an example for demonstration purposes only. The premier displacement for this engine is 350 cubic inch (CI) version. It came with a bore of 4" and a stroke of 3.48". To compute this given any bore/stroke, use the following:
- πr^2 x stroke x # of cylinders = 3.1416 x radius(squared) x stroke x # of cylinders
In the case of the 350:
- 3.1416 x 2^2 x 3.48 x 8
- 3.1416 x 4 x 3.48 x 8
- 12.5664 x 3.48 x 8
- 43.731 x 8
- 349.849 or rounded to 350 CI
As you can see, each cylinder has a displacement of nearly 44 CI. If you increase the number of cylinders to 10, you would then have 440CI instead of the 350CI in the the normal SBC engine. This is not practical for most, as to actually add cylinders would require a master machinist and a lot of tools to make it happen. So, what is left?
You can increase the bore of each cylinder. A common rebuild overage when boring the 350 is .030" (normally referred to as "30 over"). If you plug the new diameter of 4.030" into the formula, you would then have a displacement of 355CI (if all else remains the same). This is not a huge amount of gain for this procedure, but does yield a larger displacement. Increasing the bore size is the easier of the two ways to increase the displacement, but yields smaller results. Also, in a block, you can only bore the block so much, before the cylinder walls become too thin to be able to contain the combustion cycle. Most Gen I SBCs can withstand being bored +.060" over standard without too much of a problem. To go further than that, you must check the thickness of the cylinder wall to ensure it is thick enough to support what it needs to.
The other way to increase the displacement is by "stroking" the engine, or adding more stroke. To do this, there are several different ways to accomplish it. An old school way was to do what is called offset grinding of the rod journal on the crankshaft. This is done by making the journal smaller on the inside of the journal face. The outer face remains basically untouched. This may be hard to visualize, so just understand it is one method, and is not used that much any more. The more practical way to increase the the stroke is to buy an aftermarket crankshaft which has the offset built into it. There are many manufacturers which provide such components for many of the popular engines used (or reused) today. A quick trip on the internet can provide you with a stroker crank with a stroke of 3.80". This stroke, when plugged into our formula above would net a displacement of ~383CI. With only +.32" of stroke, you have gained 33CI. The 383 stroker is a common stroker engine because back in the day, smart engine builders took the crankshaft out of a 400CI SBC and put it into the 350, which yielded the 383CI. This was done because the 350 block was much more plentiful than the 400CI blocks, plus, had a lot fewer problems. There are considerations when putting larger stroke cranks in engine, the most prevalent being clearances. You have to consider since the connecting rods are now being slung out further, they run the chance of hitting some part of the block where they used to not be. The connecting rods also get closer to where the cam shaft resides as the stroke increases. You can machine the block in strategic areas to prevent contact. To keep it from contacting the cam shaft requires a bit more planning. This is not true for every engine, but for those in the V configuration it is a distinct possibility.
Another consideration of how well an engine runs (thus the power output) is volumetric efficiency or VE. In basic terms, VE is how well the cylinder fills with the air/fuel mixture. Under normal circumstances, a normally aspirated engine (one without a turbo- or super-charger ... talk more on this in a minute) is in the range of 70-80% probably. By making an engine more efficient and increasing VE, you will have a higher power output from the engine (more air/fuel, bigger bang). If you increase the VE by 10%, your power output should increase as much. This leads to forced induction (turbo- and super-charging). Adding a turbo charger to an engine effectively makes the engine "think" it is bigger than it really is. Normal atmospheric pressure is ~14psi. The engine in and of itself, is just a very elaborate air pump which produces power. The piston goes down in the cylinder, which creates a vacuum, which is filled by the air/fuel mixture. By using a turbo, you more completely fill the cylinder, getting your VE to over 100%. If you run your turbo at 14psi, you are basically doubling the amount of air/fuel into the cylinder, which in turn basically doubles the amount of power output from a given engine without increasing the size of the cylinder. Theoretically, if you have your 1000cc 4-cylinder engine, which may put out 100hp, if you do this you should have an output of 200hp. This is a very simplistic model, as you have factors involved such as compression ratio, tuning, component strength, and others, to worry about.
To understand if the engine you intend on increasing the displacement on can handle it, the easiest thing to do is check on the internet. There are forums aplenty for just about every type of engine produced. If it's out there, there are people wanting to have greater engine output. Some engines it is very easy to make modifications to, as there is a large aftermarket following. Many popular engines can be built completely with aftermarket parts. Other engines, you have to build by the seat of your pants.