Found:
 
With the same GHz Speed, The Pentium D was the slowest under most situations. But there were times where the Pentium D beaten the Core Duo  CPU because the Core Duo CPU had to wait for its Cache sharing to complete.
 
The Core 2 Duo had beaten the Core Duo hands down, and beaten the Pentium D because the Core 2 Duo has a faster data bus. But the Core Quad beaten the Core 2 Duo; making one think that a Core Duo to Core Quad would be a better upgrade option than the Core Duo to Core 2 Duo upgrade.
 
The lines blur when comparing the Core 2 Duo with the i3. The i3 has a much faster data bus and much larger cache. So for large intensive data processing that uses the cache a lot, the i3 beats the Core 2 Duo hands down. But for general computing like general office work, the Core 2 Duo beats the i3. The Core 2 Quad beats both i3 and i5 CPUs under the same conditions but here you are comparing 2 CPUs (in the i3 and i5) against 4 CPUs (in the Core 2 Quad).
 
So far the i7 stands on its own; but the Core 2 Quad is no slouch either. It's like the old argument of which machine is faster - a 700MHz PC or a 900MHz PC when everything else is the same (data bus and I/O speeds)? The answer would be that they are too closely matched for normal office work to make a difference but under heavy data processing loads, the 900MHz PC beats the 700MHz though the average user would not physically notice it. So figuratively what takes a minute to do on the Core 2 Quad, takes 45 seconds on the i7; when everything else is the same (same data bus and I/O speeds).
 
But one of the issues here is cooling hardware. One can literally heat their home with a Pentium D system when running at its fastest speeds. The iSeries still requires cooling hardware but not as large as the Pentium D. And the Core Quads/Core 2 Quads also need a large cooling system when compared to the Core Duos/Core 2 Duos. Thus upgrading the CPUs from one to another, one also has to upgrade the cooling to that CPU as well.

Now, lets add some fuel to the fire. Found:
 
When running at the CPU's rated "Official Speed" things get quirky. The fastest of these CPUs is the Pentium D running at over 4.2GHz. But running it this hard and fast makes it run hot.  The question is, is it the fastest?
 
There are problems with the Pentium D, it is 2 separate CPUs on a die, with a physcial space between them if about .5mm. .5mm does not sound like much, but it is. The two CPUs are connected together by wires and added circuitry bumps on the die. At this speed of 4+GHz one can think - "WOW! That Is Fast!" But at this speed, the laws of Physics comes into play.
 
The speed of light is 185,929.397 miles per second. But at 1-billionth of a second or at 1 GHz, that distance shrinks to about 5 inches. Electricity travels at half the speed of light, thus it takes 10 inches to travel within a a billionth of a second. This is as large as most mother boards. Circuitry slows this down even further and when you go past a certain speed, you being to lose valuable time.
 
Thus this .5mm space between the two CPUs in the Pentium D becomes a problem at these high clock speeds as the distance grows as the time shrinks. Clock cycles get wasted and the CPU is left waiting for the signal to get to it.
 
In the next series of CPUs, Intel made them together with no space between them. This speed things up by a lot. But because of this, the Core Duo and Core 2 Duo CPUs are larger chips on the die. They faced what I call Levinson's Problem.  
 
In the early 90s CPU makers ended up with a problem - at certain clock frequencies, the chip would vibrate on the die and then shatter after a while. This is why for a long time CPUs never went above 50MHz. My friend and mentor, Dr. Levinson of Rutger's U. asked me about this, and I stated, "Yes, chips do vibrate on the frequency that is pumped into it." and I gave him a demonstration of it. Being a professor of mathematics and in the field of Topology (2/3/4/... dimensional mathematics and graphics) he thought about it. And then with my help and influence he came up with the solution based on the behavior of a wave rippling through a solid - have the wave echo back so it cancels out the next coming wave. Since then CPUs shot off from 50MHz to 100, 200 and all the way to where it now in the GHz range. But he stated that the next problem will come when the speed of electricity and the size of the chip becomes an issue. This was 1992. We are there now.
 
Unlike the Pentium D, the Duo Core and Duo 2 Cores are large enough to face this problem. Being fused together as 1 CPU rescues the Core Duo chips with the issue of space/time but they face the problem of vibrating themselves apart at high GHz ranges - Levinson's problem. The Pentium III also had this problem, and Intel's solution then was to back down the clock speed on the CPU. Thus there are no official Pentium III faster than 1.6GHz though they can run faster than 2.25GHz. They did the same thing with the Core Duo and Core 2 Duo - officially rating them for no faster than 2.8GHz. Anything faster than that and they will not recognize the warrantee, and they know the pattern the chip will shatter for a given over-clocked speed.
 
So here, a Pentium D running over 3.5GHz will beat a Core Duo/Core 2 Duo running at 2.8GHz. The only saving grace here is that the Core Duo/Core 2 Duo has a faster data bus speed, this information from the rest of the computer will get to the Core Duo/Core 2 Duo than it will to the Pentium D. This becomes a race where the chips are faster in one area than another. In truth, in this respect they are about even, though the Pentium D is running faster. And the Pentium D running faster runs hotter so it will require more cooling hardware.
 
Until recently, the iSeries (i3, i5, and i7) were also speed limited to 2.8GHz. So between the Core Duo/Core 2 Duo, they run about the same speed. But being on a smaller smaller and with larger caches, the iSeries beats the Core Duo/Core 2 Duo CPUs. Only recently they are pushing the i5 and i7 into the 3GHz range, making them unbeatable. But currently, laptops are either iSeries or Core/Core 2 series no faster than 2.16GHz, and Desktops up to 2.8GHz. So which one to get?
 
The problem here is the Core Quad/ Core 2 Quad CPUs. Running at the same speed, they beat the i3 and i5 CPUs. Against the i7, the Core 2 Quad was just a bit slower. The iSeries saving grace is that they have a faster data bus speed and this is where they beat the Core Duo/Core 2 Duo series. But in a system where the data bus speed is the same between the two CPUs, it is barely noticeable.
 
Intel's mistake is making most of these chips socket compatible with each other. In theory one can take an i7 CPU and slap into a Pentium D mother board. It wont work because of conflicting data bus speeds, but it will for the Core 2 Duo with the same data bus speed. The same with the Core Duo/Core 2 Duo with the Pentium D if the data bus speeds are the same. And the Core Quad/Core 2 Quads with fit into either board as well as long as the data bus speed matches.
 
There are socket specific CPUs Intel made, but for some reason they decided to give the public a chance to upgrade with some of those CPUs with the same socket across the CPU generations from the Pentium D to the I Series.
 
What about the single core Pentium 4, which these multi-core CPUs are based on? The Pentium 4 was pushed officially 4.25GHz as well, making it no slouch for basic PC office work. And they are pin/socket compatible with some of the Pentium Ds, so an upgrade here is possible. But compared to the other CPUs Intel makes, besides the Core/ Core 2 series and iSeries, there are several with 4 and 8 core CPUs. They are mostly used in server environments and not for the general public. And these other chips are not Pin/Socket compatible to the those released to the PC using public either.
 
But again, in upgrading the CPUs in these personal systems, you need to upgrade the cooling hardware.
 
One area where people are running into is the Mac Mini Apple Computer. The 2005 version uses the Core Duo, and the 2008 series uses the Core 2 Duo, but many out there swap out the CPU as a cheap upgrade. Then they end up with a Mac Mini that runs hotter than before. More so if they swap out the Core Duo with a Core 2 Quad CPU. The Mac Mini is too small for such an upgrade unless you take the heatsink from the '08 Mac Mini and put it into the '05 Mac Mini. I have one of those cheaply upgraded '05 Mac Minis. It runs very hot so I do not run it often or for long. I'll use my powerbooks or my other un-upgraded '05 Mac Mini.

Oddly enough, the older AMDs beat the Intels. 1) Larger Cache and 2) CPU Cores are connected together as 1 core. With the iSeries, the AMD are tied with Intel if the Core Count is the same but AMD has CPUs with higher number cores for the public while Intel only has them for Server Systems only.

There's an 8-core AMD out there for PCs but you will never see that in an Intel PC! Not yet.
 
And your 3 core AMD beats nearly all the dual cores Intel makes.