I think this is a well known fact nowadays and various sims feature it. Helicopter trim mechanisms are different but the example that readily pops to mind is Black Shark, where you trim by setting the stick where you want it (ie, selecting an attitude for the aircraft) and pressing the trim button. This sets the default stick position to where it was when you pressed the trim button, which effectively lets you fly without applying constant pressure.
If you have a force feedback stick, its position matches the position of the in-game/virtual stick. If you don't have one though, it still works this way by defaulting the centered position of your spring-loaded stick to the off-center position of the virtual one.
I think the difference lies in the fact that in the helicopter the trim mechanism applies force to the collective to keep it at a certain position, which then transfers to the stick through the linkages.
In an aircraft however, trim moves the trim tabs which then move the control surface through aerodynamic interaction and then that movement is transferred to the stick through the control linkages.
In the end the result is pretty much similar, it's just the "how" that changes.
Also, the trim oscillations you guys mentioned are interesting. I don't have any real flying experience, just comparing my sims and FSX which i fly on a friend's PC when i visit him. Since most 3rd party payware aircraft for FSX are so much more detailed than the stock models but also feature a lot of differences between them in modelling (depending on developer), i can't be sure how pronounced the effect should be.
However, it's interesting that in certain airframes it's more apparent than in others. So, i might trim nose down for cruise after i reach my selected altitude, but after a while the aircraft still wants to climb because it has picked up speed as a result my down-trimming, which necessitates further nose down trim on my part to keep it level. However, if i dial in the necessary trim in one motion, the resulting down pitch from climb to cruise is so big that i can't pick up speed fast enough to keep it level. This forces me to trim in "stages", dialing in a bit of trim to zero the vertical speed indicator and adjusting as necessary a few more times until it settles in.
To make all this easier to manage, i stopped thinking of trim as a way to keep my nose at a certain angle to the horizon and also stopped thinking that nose up=climb all the time. In fact, there are cases where you can be nose up and descending, or cruising level at a certain altitude and yet have a nose down attitude.
This nose down attitude is more pronounced on aircraft that cruise "on the step" as the saying goes: it's better to climb at X+500 feet of altitude and descent to your chosen X altitude, trimming as you go, than climb to X altitude and level off straight away.
In FSX i've seen it on a B17 and a Boeing Stratocruiser (both 3rd party payware aircraft). This is also evident in IL2, anyone who flies the Fw190 knows that it can cruise faster this way at the same power settings.
In the end, what makes the difference in the whole process is the airspeed you maintain and the power you run your engines at.
Wing design and angle in relation to the fuselage all have a factor in this, but generally speaking i've found that the best way to think of trim is that it tells the aircraft to maintain a certain airspeed. If the aircraft can maintain this airspeed at the power settings it's currently running, then it will fly level. If it can't reach that airspeed it will nose down to achieve it. Finally, if it exceeds this airspeed with the chosen power settings it will climb to bleed off some airspeed and reach that value.
It's almost like the opposite of a car: when going uphill you apply more throttle than when going downhill.
In an aircraft where you can move in 3 dimensions, the reverse thing happens: apply enough throttle and the aircraft will make its own imaginary "hill" to climb.
Anyway, i'll leave this here since my excitement about the mechanical intricacies of aircraft is already getting my side-tracked from the topic into analogies and trim mentality discussions
I think that since various modern sims have a more true to life representation of the transfer of aerodynamic forces from the control surfaces to the stick (DCS, RoF, FSX, etc), it will probably be something that SoW has paid attention to as well.