This subject has been spoken about many, many times. Please use the search function for your future questions, and if you do not find an answer, then post a thread. Many people will come in and tell you to search, so be prepared.
Starting now, forget comparing the cpus of AMD and the cpus of Intel via clock speed. ONLY use clock speed as a reference between processors within the same company. For example, a 3.2Ghz Pentium 4 is faster than a 2.8Ghz Pentium 4. A 2.4Ghz Athlon 64 is faster than a 2.2Ghz Athlon 64. Do not compare the Mhz of AMD to the Mhz of Intel, or you will become confused.
Yes, the differences between clock speed are quite large. The reason for this is because the processors are based on completely different architectures. A 1.8Ghz Athlon 64 compares to a 2.8-3Ghz Pentium 4. The differences between them are FAR too great for me to list here within any reasonable amount of time.
If you want to do some rather lengthy reading for a true answer, than here are some indepth artices on the AMD64 architecture.
http://www.anandtech.com/showdoc.aspx?i=1815
http://www.anandtech.com/cpuchipsets/showdoc.html?i=1816
http://www.anandtech.com/it/showdoc.html?i=1817
http://www.anandtech.com/cpuchipsets/showdoc.html?i=1818
http://www.anandtech.com/showdoc.aspx?i=1884
Those links are in order of what you should read first, starting at the top.
The easiest way to go about it without much research is to look at AMD's model numbers. In general, you can expect them to be correct for general usage. An Athlon 64 3200+ can compare to a Pentium 4 3.2Ghz(3200Mhz). An Athlon 64 3500+ can be compared to a 3.5Ghz Pentium 4.
Things get confusing when you start talking about dual cores. AMD's Athlon 64 X2 4800+ is dual 2.4Ghz cores. This would not be the same thing as a 4.8Ghz Pentium 4. For information on dual core processors and SMP in general, I recommend here:
http://www.ocforums.com/showthread.php?t=126186
On average, 99% of the people on this forum will recommend AMD over Intel. I agree with that. An Athlon 64 3200+ normally is faster than a 3.2Ghz Pentium 4 in just about everything. Sometimes by a lot, sometimes by a very little bit, but it usually comes out on top. This can pretty much be said about all the model numbers.
Since you are going to build a new computer, I HIGHLY recommend you build a dual core machine. The benefits of a dual core machine are huge. For example, with a dual core, you could burn a cd/dvd while playing a game with no drop in performance. You could encode media while playing a game without a drop in performance. You could scan with an antivirus and play a game and not have a drop in performance. You can do pretty much any cpu intensive task, and still have an entire other cpu core available for something else.
I hope this helps a bit.