It always amazes me how otherwise intelligent people who are usually completely honest about what they know or don’t know can spew out the most random junk about computers. I try to comfort myself with the thought that most of these people who don’t know what they are talking about are doing just fine with the system they got.
But if you want the real skinny, do yourself a favor and check out hardware central (mentioned above) or www.anandtech.com (my personal favorite. I don’t like tomshardware, because his benchmarks usually look suspiciously different from all the other sites.
Here’s a quick answer to the actual question asked:
The price difference is mostly due to that “Intel inside” sticker on the front of your case. In general terms K7(Athlon) kicks the pants off of Pentium3. Celeron when running at a comparable clockrate (500mhz vs 500mhz) does just about as well as a Pentium3. K6-2 and K6-3 do about as well as comparable clockrate Celeron/P3, and better for those applications which are optimized for them. All these chips have cache, in varying amounts and configurations. P3, K7/Athlon, and K6-2/K6-3 have special instruction sets (mmx2 for p3, 3dnow for AMD stuff).
And the most important fact of all: If you are an average user (email, websurfing, occasional Office document), they will all have more power to spare than you will use.