I have Nakamichi
CM 300 [snip] also a microphone preamp The CM 300 output is too low for the Zoom recorder internal mic preamp. I could use my home built preamp and input "line level" unbalanced to the zoom or buy some new mics. My nephew (into recording) recommends AT 4041.
The Nakamichi is back electret (permanently charged) style of mic that requires a specialized battery (and fairly hard to find anymore) and without modification does not accept phantom power. (this might or might not have something to do with problems with hand held recorders running on batteries) the CM300 would have been a very reasonable mic (if found at right price) 30 yr ago similar to Audix Uem81 (a back electret marketed as lower cost competition to Shure SM81) and the newer AKG low cost C1000 which was marketed as a handheld condenser (back electret)
whether using the pre-amp (and attendant power issues) complicates use of existing mics for field/live recording too much is, of course, only something you can answer. Having used both (got rid of CM300's rather then having the modded for phantom, never used them much in any case) my opinion is that the AT4041 is a superior mic. The nice thing about the CM300 was that they came stock with two capsules, cardiod & omni. That option, at the time I more or less inherited them from a battery frustrated acquaintance, was useful. Omni's tend to get less love from home recording field practitioners but can be quite useful (particularly if you want to avoid stereo boondogels but still what to capture a 'broad' sound scape) Having the choice on the same mic body was useful for things similar to small venue low(er) volume, quieter crowds situations. If the room would support it the omnis were frequently the way to go.
As I got more sophisticated (at least in my own mind) I migrated to other mics: K84 (and variations) AKG c451 (and variations) even the Shure SM81. Recently, for me, I have picked up a pair Josephson C42s that I like and depending on options for auditioning I would certainly suggest as one to try.
While it is seldom a good idea to buy a mic sight unseen (heard) I do have enough experience with Audio Technica in general and the AT4041 specifically (bought one sight unseen (heard) from an early internet retailer because I was sure they listed it as an AT4051 and the price was just too good to pass up . . . I already liked the AT4051 enough to get another (2) @ the listed price and then liked the AT4041s enough (though still believe 51 to be better over all) that even while the price was not quite as exceptional kept them (mostly, initially, to avoid protracted fight with retailer, though never purchased anything from them again. sadly they are still in business))
I have a
Zoom H4 (not 'n') and the AT4041 works fine with it. I actually used it to record piano for a couple of low rent recital projects in fairly difficult rooms . . . small, overly reflective with pianos that were too large (for the room) overly 'bright' (in my opinion) with an action that was too loose for the pianists playing. For all the issues the client claimed they were happy. Perhaps it goes without saying that there was significant difference between initial test recordings of piano/room from onboard mics and AT4041s
I would expect the CM300's to also display an improvement over the onboard mics (not attempting to trash those mics for cost of machine they are not as bad as they could have been but for relatively small increment in manufacturing cost they could have been better)
If you can live with having a mic pre in between the mic and recorder it really depends on whether you want to update your mic locker as to whether you update that locker . . . once you start on that path there are very few people who can stall at only a single mic . . . if you catch the but mics are one of the most addictive pieces of gear out their (and I'm someone who tends to acquire non collectible guitars and modifies potentially collectible ones to make them non-collectible)
in any case good luck