I doubt I have anything to add that wasn't already mentioned, but....the original CoD was pretty much a spiritual successor to MoH:AA (a big reason why people were excited for CoD back in the day was precisely because it was being developed by the former 2015, Inc. guys who worked on MoH:AA). So in a lot of ways, CoD 1 was basically a more refined MoH:AA. Both of them even used the Quake III engine.

If I really had to say which one is better, I think, overall, it was CoD. Not only did it benefit from the lessons learned from MoH:AA, it also featured a greater variety of weapons and battlefields. Granted, having the game show the British and Soviet perspective isn't anything special nowadays (although I lament the fact that, to this day, no FPS game has featured an SP campaign focused on the members of Axis armies), but it was unheard of at the time. Also, the multiplayer was better.

That said, this isn't to say MoH:AA isn't worth playing...and not just out of historic interest. It shares a lot in common with old school shooters in that you're basically one man army tasked with fighting entire groups of German soldiers. As such, in spite of what I said at the beginning, there are some minor differences in their appeal.

The interesting thing about both these games is that their respective expansions took cues from competitor games. United Offensive made CoD more similar to Battlefield (this change of direction kind of ended up splitting the community, which is why both vanilla CoD and UO continued to live on side by side), whereas Spearhead was essentially CoD if it were developed by another studio.

Lastly, as a side note, both games had awesome music. While I think too many video game composers seem to think that orchestral music is epic simply because it is orchestral (sadly, a lot of the time, it just ends up being generic and dull), MoH:AA and CoD are among the better examples that use this style of music. The MoH:AA main theme and "Pegasus Bridge" in particular remain some of the most iconic compositions within PC gaming:

https://www.youtube.com/watch?v=-ELFxB-tGhE

https://www.youtube.com/watch?v=V0ZlMXkzUqI

Honestly, that was probably intentional on their part, considering how big that movie was during that time period (and it arguably still counts as one of the best movies that involved Steven Spielberg and Tom Hanks).. This is no doubt the same reason why CoD featured "shellshock" (this isn't a correct term, since shellshock was used to describe what is today known as PTSD, but that's still the term that was used to describe this feature).

Would just like to add something to your post, the music. The music in MOHAA and CoD while suitable made the pacing of those games very "gung ho" if you know what I mean, in RTCW the music was a lot more tense and I found that improved the atmosphere considerably. The title screen music was ominous and set a very dark tone to the game. I still remember the music in the first mission where you have to excape from your cell, it set the perfect amount of tension. However, the one issue I have with RTCW is the whole "demonization of the nazis" thing which happens a lot in western entertainment mediums and I do get a little tired of it. Lots of historic events (not just WW2) have a political slant to them so sometimes it can be hard to seperate the truth from the fiction but it's especially bad in WW2 that I just don"t know what to believe anymore. Cos if that, anything with "dem evil satan worshipping nazis" in it to me just comes off as allied political propaganda. In MOHAA and CoD1, the germans were simply one side in a war, no underlying political bs and I appreciated that.

Back on topic though, I would take CoD1 for the reasons others already mentioned. Both games had the same development team and once MOHAA was finished, they could look back on the finished product to see where improvements could be made and I thought they did a bang up job.

Thanks for adding that about the music, you put it better than I would have. You raise a very good point on that, RTCW's atmosphere would just not be the same without the music which accompanied it.

I kind of agree with your Nazi point, but in this particular case I thought that it was mostly just to lend a sci-fi feel to the game. Also, they didn't seem so devil worshiping as experimenting in genetic engineering and resurrecting the dead and weird stuff like that, like a B SyFy movie plot. Doesn't help that Himmler and fellows like that kind of did dabble into stuff like that, so the temptation to write something around that would be pretty hard to resist if I were attached to the project.

Edit: It's a popular point that some members of 2015, Inc had worked on COD so I just want to draw some light to another game made by the studio themselves: Men of Valor. I don't own the game myself (would love to though) but the demo was fun and it was made by 2015, Inc. It's set in the Viet Nam War and has generally solid mechanics and used a pretty decent engine for the time (Unreal Engine 2.0, and it allowed for more action oriented gameplay (unlike Vietcong) comparable yo MOH:AA, more or less. Just saying.

Both are pretty solid, but I give a slight edge to Medal of Honor for a bit more variation in some spots compared to Call of Duty.