If you look through the Wayback machine, you can probably find details of battles between those two. Chessmaster 9000 was published in 2002 and Fritz 8 was published in 2004.
Chessmaster as strong as Fritz?

I believe that Fritz 8 was stronger than CM9000, but not by very much. I suspect that either CM9000 was lucky in those three games, or CM was using more PC resources than Fritz. (Check that they're using the same hashtable size, the same CPU resources, and the same pondering state.) And you literally have to play hundreds of games to get any accurate elo difference between the two engines.

Here's an archived CCRL 40/40 page from Feb 2008: https://web-beta.archive.org/web/20080217063807/http://www.computerchess.org.uk/ccrl/4040/rating_list_all.html
It lists a Fritz 8 Bilbao as 2800 elo, and a CM9000 Enforcer as 2758 elo. (I'm guessing that the Bilbao and Enforcer personalities gave some small performance boost over the default personalities.)
Also, here's an archived CCRL 40/4 page from Feb 2007: https://web-beta.archive.org/web/20070222170646/http://www.computerchess.org.uk/ccrl/404/rating_list_all.html
It lists Fritz 8 as 2742 elo and CM9000 Enforcer as 2740 elo.
Currently playing a match between them on two different computers! It was claimed by some that Cm is a "resources hog" but that has been strenuously denied by the developers.
I'm starting to think though that your computer's performance can make as much a difference as the program itself. For example you could have the greatest hi fi system in the world but it will still sound bad if it's played through a cheap pair of speakers.

I'm starting to think though that your computer's performance can make as much a difference as the program itself. For example you could have the greatest hi fi system in the world but it will still sound bad if it's played through a cheap pair of speakers.
For sure. If one PC has a much better CPU than the other PC, you're giving an unfair advantage to one of the engines.
Well, Fritz 8 won that one, and I used a more modern computer to use it. A laptop, granted, but with still much greater processing power. I'm almost embarrassed to say that my desktop computer (the one I played Chessmaster on) is from 2001! It uses WIndows ME, has a 1.2 Ghz CPU and has 128 MB Ram. So that further reinforces my belief that a programs playing strength depends to some extent on what computer is running it.
So in a nutshell......I'm more confused than ever!

Well, Fritz 8 won that one, and I used a more modern computer to use it. A laptop, granted, but with still much greater processing power. I'm almost embarrassed to say that my desktop computer (the one I played Chessmaster on) is from 2001! It uses WIndows ME, has a 1.2 Ghz CPU and has 128 MB Ram. So that further reinforces my belief that a programs playing strength depends to some extent on what computer is running it.
So in a nutshell......I'm more confused than ever!
If you're running a 2-PC tournament, the ideal solution would be to run a benchmark on both PCs to find the cpu performance difference. To do the benchmark test, maybe you could run the Stockfish "bench" test in console mode. Then you'd have to limit the cpu performance of the stronger PC. I've never had to do this, but there's a cpu utility that supposedly does this: https://lifehacker.com/bes-limits-how-much-cpu-power-windows-processes-can-use-1730469750
The other approach would be to import the Chessmaster engine into the Fritz 8 GUI and run the tournament directly in the Fritz GUI. However, you'd have to use a Wb2UCI adapter for the Chessmaster engine, and I can't remember if I was ever able to successfully import a Wb2UCI adapter into a Fritz GUI.

Here's another metric. It's the SSDF "long" list of ratings. It's probably the best data available for this particular comparison ---->> http://ssdf.bosjo.net/long.txt
CM 9000 is number 92 on the list with a rating of 2706; Fritz 8 is number 77 on the list with a rating of 2754. These ratings are close enough that anything can happen in a short match. Deep Fritz 8 is number 66 on the list with a rating of 2780.
So ... the information we have indicates that Fritz 8 is somewhat stronger than CM 9000 but not by a huge amount.
Edit: To conclusively prove that one engine is stronger than another, when the engines are this close in strength, takes hundreds of games. You can't draw meaningful conclusions from just a handful of games.
Okay that's cleared things up a bit. Fritz is generally a bit stronger, but a lot depends on the quality of the machine you run the program on!
So I'm glad to own programs but generally I prefer the Chessmaster series. The overall aesthetics are more appealing and best of all the opponents are more customizable. I'm not too concerned that the strength of Chessmaster is a "mere" 2700 Elo or something (and maybe a tad higher in t Chessmaster 10), that is plenty strong. GM level, or at least master level if you want to take the ratings with a pinch of salt. We seemed to have gotten spoiled a bit with computer chess these days. I remember in the 90s the strongest commercially available program was IM strength and was very expensive. Now you can pick up a GM level program on Amazon dirt cheap!

Today, I finally reinstalled my old Fritz 8 program that used to be on my previous computer. For grins, I decided to make an attempt at importing the Chessmaster 9000 engine into Fritz. It took some work, but I finally got it done. I just started up a 40/40 tournament between the two engines; I hope I get something close to the expected result.
Alright I know that these days there are ultra strong programs like Stockfish and Rybka that can be used, but I have little interest in those. Admittedly partly because I have an ancient PC that hasn't the system requirements to play them.
But the added strength of these programs is overkill to me, at least from a playing perspective. I have Chessmaster 9000 and 10th Edition, and Fritz 8, both programs from about the same era. These programs are plenty challenge for me!
The Chessmaster series has often been regarded as the less serious, more accessible one, while Fritz has the reputation of being more serious and stronger at the expense of a colder, more functional interface. I accepted that as fact until in the past few days I actually paired Chessmaster 9000 and Fritz 8 against each other using tournament time controls (40 minutes per 40 moves) Chessmaster won all 3 games they played. And I mean it had a large advantage by move 45 or so, say connected passed pawns, or an extra pawn. I was surprised. I was expecting the opposite to happen.
Just a fluke? Or is Chessmaster really the equal of Fritz? The Chessmaster 9000 program claims a strength of 2761, but I know these figures should be taken with a pinch of salt.