While Sony does consider the PS3 a "computer system", it is not built like a typical computer, as the PS3 is not required to be able to do multiple things like a computer would be. Not only that, but everything that is made for the PS3 is made specifically for the PS3, which means, if it doesn't work, then it has to be redone. With a PC, if it doesn't work, that means you need to upgrade your PC.
With all of that said, the PS3 does have a motherboard, (not conventional PC) processor (actually, processors), and a (not conventional PC) graphics card. Here are the PS3 specs:
Graphics Card - The PS3 uses the RSX GPU, which is based on the nVidia 7800GTX graphics processor, and is a G70/G71 hybrid (the PS3 version is a scaled down version of the nVidia version).
RAM - 256MB (this has always been a concern for PS3 users, as it is thought that the PS3 should be made to utilize a higher RAM).
Processor speed and type - The PS3 does not use a traditional CPU like a computer, it has a Cell Broadband Engine, which uses several different components, one of the reasons the military used multiple PS3s to build a supercomputer, it was cheaper than actually building a supercomputer from PC parts:
The Cell CPU has one 3.2Ghz PPE (Power Processor Element) with two threads and eight 3.2Ghz SPE (Synergistic Processing Elements). The PPE is a general purpose CPU, while the eight SPE are geared towards processing data in parallel. One SPE is disabled to increase yield, so the PS3 can have at most 9 threads running at the same time (2 from PPE and 7 from SPE). Note that one SPE is reserved for the hypervisor, so PS3 programs can take advantage of 8 threads. The Cell was introduced at 90nm and later PS3 model numbers starting with CECHG uses the 65nm version.
1 PPE (Power Processor Element)
2 threads (can run at same time)
L1 cache: 32kB data + 32kB instruction
L2 cache: 512kB
Memory bus width: 64bit (serial)
VMX (Altivec) instruction set support
Full IEEE-754 compliant
8 SPE (Synergistic Processing Element) only 7 available for use
1 SPE disabled to improve chip yield
1 SPE dedicated for hypervisor security
256kB local store per SPE
128 registers per SPE
Dual Issue (Each SPE can execute 2 instructions per clock)
IEEE-754 compliant in double precision (single precision round-towards-zero instead of round-towards-even)
As far as comparing your PC to the PS3 for gaming potential, that is not realistic, as PC games may require different requirements, where as PS3 games are all made to work with the PS3 hardware. While an old PC game like Assassin's Creed may work on your PC, that doesn't mean the new Assassin's Creed: Brotherhood will, whereas with the PS3, both games will work on the PS3, because the developer is forced to work within the parameters of the PS3.
When the PS3 was first released, it was considered to be equivalent to a high-end PC. As everyone knows, technology moves fast these days, and it can literally be only a few weeks before hardware can become outdated.
The PS3 is no longer considered a high-end PC (the price can tell you that), it is now more on par of a Low mid-range to High low-range PC.