Is it true that the Mac G4 processor is twice as fast as a Pentium III?

It is true that the G4 is faster than the Pentium III on many
tasks. For example, if you run the SETI@home screensaver
(which uses lots of floating-point calculations to perform
signal processing operations on radio telescope data), a G4
running at 500 megahertz (MHz) will produce a result set in
about half the time of a Pentium III running at 700 MHz. This
is a remarkable difference in processing capability.

When creating a microprocessor, the designer gets to make
millions of decisions. A basic limit in the design is the
number of transistors that will fit on a chip, so the
designer is trying to make decisions that obtain the best
performance from those transistors. The designer may also
have to worry about backward compatibility with older
instruction sets and looming release dates.

For example, the Intel 8080 processor took something like 80
clock cycles to multiply two 8-bit numbers. It took so long
because the number of transistors was severely limited at the
time the 8080 was released. Today's processors can often
multiply two pairs of 32-bit numbers in a single clock cycle.
The difference between then and now is the number of
transistors -- a greater number of transistors allows more to
happen in a single clock cycle.

If you look at Motorola's documentation, it says that the G4
processor features:

a high-frequency superscalar PowerPC core, capable of issuing
three instructions per clock cycle (two instructions +
branch) into seven independent execution units:

o Two integer units
o Double-precision floating-point unit
o Vector unit
o Load/store unit
o System unit
o Branch processing unit

The­se execution units feed off of a 128-bit internal bus.
The feature that gives the G4 most of its speed in SETI@home
processing is the double-precision floating-point unit. The
G4 can complete one double-precision calculation every clock
cycle, while the Pentium III cannot.

The G4 also features an interesting vector processing unit.
Applications must be specially coded to take advantage of the
vector processor, which allows them to perform certain
mathematical operations very quickly. A vector processor
executes the same operation on multiple pieces of data at the
same time. In the G4, up to eight simultaneous operations can
execute in a single clock cycle in the vector unit. This sort
of processing power is what makes the G4 so fast when working
with math-intensive applications like Photoshop that have
been coded to take advantage of vector processing. The
Pentium III features a vector processing capability as well,
but it is not as powerful.