Difference between PCI and PCIE (x4,x8,x16)?

What exactly is the difference between the two types of PCI slots and are there benchmarks to show there is a marked difference between them? Added benefits? 

PCI is older than PCI-express, and pretty much all graphics cards use PCI-express, and the most recent ones use the 3.0 revision. x1, x4, x8, and x16 refer to the amount of bandwidth the slot can handle, and it can vary according to how many devices you are using since the CPU or mobo chipset (not sure which, might actually be both) affects the total number of PCI-e lanes available.

I assume you're talking about graphics cards. Pci-e 3.0 running at x8 or x16 will not have any bottleneck, and pci-e 2.0 @ x16 can run a pci-e 3.0 card with no bottleneck. pci-e 2.0 x8 will result in usually a minor bottleneck, but you sometimes have to run slots at x8 when using SLI/CFX

I will just say right now that I might not be correct in terms of the relation of bottleneck and slot bandwidth.

They are very very different.

For starters, the connector is different. PCI and PCIe cards are not interchangeable. Electrically they are different. PCI is parallel and PCIe is a serial connection. 

As for benefits? It is much faster, lower pin count which results in a smaller slot, better performance scaling, error reporting and correction, and it is hot-pluggable and can polymorph into a whole variety of different interfaces like Express Card and Thunderbolt. 

The biggest and most important difference is speed. 

A PCIe 3.0 X16 lane can max out at around 16 GB/s. PCI can hardly mange 500 Mb/s. A modern GPU would never be able to work on conventional PCI. It just doesn't have enough bandwidth. 

As for the numbers you are talking about, PCIE has a number of lanes (basically a connector that can handle a certain amount of data). PCIE is scalable so you can add as many lanes as you'd like to get the speed you need to a max of 16 lanes. The number refers to the amount of lanes you have. The more lanes the higher the speed. The slot will also be longer. 

So an X1, is smaller and slower than an X4, which is smaller an slower than an X8, which is smaller and slower than an X16 PCIE slot. 

The cool thing is though about PCIE is that any PCIE card (as long as it isn't limited by bandwidth) can work in any slot.

Say you want to plug in a WIFI adapter. It only needs an X4 lane but you don't have any x4 lanes available. You could plug it into an x1 slot, some of the card would hang out the back of the slot, it would work but it would just be slower. You could also plug it into an X8 or an X16 slot. It wouldn't fill up the entire slot but you'd get the full speed of it. PCIE gives you flexibility. 

There are also different versions of PCIE. PCIE 2.0 and 3.0 are the most common right now. 3.0 is faster than 2.0. But they are compatible with each other. You can plug a PCIE 3.0 GPU into a PCIE 2.0 slot and it will work just fine. It doesn't matter than PCIE 2.0 is slower because most modern GPUs can't even fully saturate a PCIE 2.0 X8 lane right now. 

The PCI-e bus lanes are restricted by the number of available bus lanes on the CPU. This is why people like socket 2011 chips, they have many more bus lanes within the CPU, so you can actually do triple crossfire/SLI.