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The Xilinx Virtex-4 FX FPGA has a PowerPC processor permanently embedded in the silicon. You can also temporarily configure a processor (such as MicroBlaze) in the FPGA's reconfigurable logic fabric. I suppose you could call those "hardcore" and "softcore" processors.
Basically you are right, but consider that the Power-PC costs you extra money in a price of the FPGA chip, while the MB can be implemented in almost any FPGA at no extra cost. You can even put multiple MBs in a single FPGA if you like.
There are always some trade-offs.