Faster is a relative concept. The minimum processor for running Rhapsody for PowerPC is a PPC 604 at 120 MHz. A G3 at 233 MHz is way faster than that.
When I was running Rhapsody on my Wallstreet it was fast enough to do everything I wanted with a G3 at 266 MHz, but so is my ThinkPad with a Pentium at 133 MHz. My fastest Rhapsody system I have right now is a PowerMac 7500 with a PPC 604e at 225 MHz, which is great (I even play Quake II on that system).
As with Mac OS X, memory plays the biggest role in overall speed. While my 7500 was very responsive for simple tasks with the original 80 MB of RAM I had in it, when I wanted to to a page layout project in Create that used tons of graphics and was about 15 pages long, the system slowed down dramatically and even the smallest changes had me watching a beach ball. When I jumped it up to 208 MB I no longer had any problems (it is now at 512 MB, but there wasn't as noticeable a change as I haven't taxed it to the point of needing that much memory).
Now if you plan on using Blue Box a lot, more memory is better. While 64 MB is fine for just running Rhapsody and some of it's apps, I would suggest no less than 128 MB if you plan on using Blue Box a lot (I don't even have Blue Box installed on any of my systems anymore).
For a Wallstreet you need a minimum of Rhapsody 5.3 (Mac OS X Server 1.0), Rhapsody 5.0 & 5.1 won't run on that system (as they predate it and the technology in it).
As for what you can expect... well, Rhapsody is 100% PowerPC native while Mac OS 8.1 isn't. So it should run faster. I would guess that even Blue Box (which is Mac OS 8.5 or 8.6) would run most all tasks faster than Mac OS 8.1 as more of that code is PowerPC native.
When I was running Rhapsody 5.6 on my Wallstreet, the original 192 MB of RAM was fine for all my Rhapsody tasks, but not so great when you added Blue Box into the mix. I later upgraded the system to 512 MB.
Another thing to keep in mind is that when you are thinking of how fast a system is going to be relative to another system, that is assuming that you are going to be doing comparable tasks with the systems you are comparing.
What are you doing now in Mac OS 8.1 on that system? Is there software for completing those tasks in Rhapsody? Is that software different enough that it is going to take time to learn how to use it effectively?
See, for me, my core base of applications is pretty much the same from OPENSTEP to Rhapsody to Mac OS X. OmniWeb, Create, PStill, OmniDictionary, PhotoToWeb, ToyViewer, PixelNhance, TextEdit, RBrowser and Preview are examples of apps that exist on all three and are a major part of my regular work flow.
An example of a conflict I run into is image editing. I use Photoshop on Mac OS X a lot, but there isn't a version for OPENSTEP or Rhapsody. This means I have to use something else... TIFFany. And TIFFany is very different from Photoshop, so it is faster for me to work in Photoshop (even on a slower system) than it would be to do the same task in TIFFany.
And an example of finding reasonable alternatives is diagramming software. In Mac OS X I use OmniGraffle, in Rhapsody there is GlyphiX, and in OPENSTEP there is Diagram. They all work pretty much the same (and OmniGraffle can even open Diagram documents).
As you can see, there is a lot to all this. My primary application in Rhapsody is Create (which is about $150). I can do illustrations, page layout and web design (my Rhapsody site is made in Create on Rhapsody) with it. That is a lot of bases covered with one app, so it is very helpful.
This is also why I try to cover a lot of these types of things in my web site. If you just load Rhapsody and nothing else, then all you have is an OS... you can't do much with just an OS. You need applications to be productive, and being productive is the best measure of speed I can think of.
And as you can guess, I'm very productive in Rhapsody.