Pentium 3 and Celeron D.....

If you want to compare Pentium 3 and Celeron D for the stornger one.
It is Celeron D, as Celeron D is the CPU is created from the Pentium 4.
The differences between Celeron D and Pentium 4 are the size of L2 Cache and speed of FSB. (We can say that Celeron D is the Pentium 4 with error in L2 Cache)
For Pentium 3, the Architecture and the technology used are outdated comparing with the Pentium 4 (or Celeron D).
Both of them are used for doing office work, if you got a Pentium 3, it's not necessary for you to upgrade to Celeron D (as this have to upgrade the whole system, upgrade to a more powerful CPU like Pentium D or C2D is better.)
If you want to say the strongest CPU of desktop, it is the Quad Core QX6700.
Someone always say the Xeon is better, but it is wrong. The reason why Xeon is so expensive is the support in multi-CPU. Although QX6700 is strong, the performance can fight down 2 Xeon used together, Xeon can still upgrade to 3 or even 4 Xeon, that can fight down QX6700. That's the reason.

I've used 3PCs using Celeron D, the performance is not bad!
It's FSB is faster than and cache is as large as early P4; (533Mhz vs 400MHz, both 256KB)

I have personal experience on these two CPU chips but already shifted to updated and more powerful chips such as P4, Centrino & Duo Core.
It depends on what kind of application your are interested.
For general purposes such as Word and and emails. I prefer Celeron D...
For special appliaction, try Pentium 3 even though it is older than Celeron.
It seems that you do not want to upgrade or making use of the existing facilities to save cost. My experience is that leave your existing Pentium 3 machine to handle fax receiving for commercial consideration and let it run all the day. Do not hook this special purpose machine with your main system to avoid being virus infected because of outside connections at 24 hours. Do not spend additional resources on improving the P3 machine and it is really not justify to do it.
If you want more powerful performance, you better buy an entire new machine.