Bobdobalina,
My experience with ME66/64:
I bought the ME66 in 2002 (later added an ME64) to go with a Canon XL1s standard def video camera. I got it instead of the 416 to save $500 because I was tapped out money-wise and as a camera person, didn't think too much about the difference between the 2 mics. 14 years later I still use the ME66. But only as a scratch track or back up mic.
It is my biggest purchasing regret ever.
Only later when I really used superior Schoeps, Sennheiser, and Sanken mics did I realize how tinny the ME66 is. When I prorate out that $500 I saved over the past 14 years. I basically saved $35 a year for a relatively so so mic. When I think of all the mediocre audio I recorded over the years to save $3 a month, I see what a bad decision it was.
That was 4 cameras ago yet the ME mics are still with me due to good German engineering. Be they good or mediocre, mics are truly long-term investments. Knowing this now, I am willing to spend as much on mics as cameras since I know they deliver greater value in the long run.
Given that you are on camera with the mic, (sounds like run and gun) it seems like you could be in all manner of uncontrolled audio environments. Here again, a 416, a Sanken cs3, or Schoeps CMIT 5 will save you whereas the ME66 will fail you (Schoeps CMC641 for indoor audio).
If you rent these mics, side by side them, the ME66 I think will be very disappointing to you. You might even be able to go into an audio vendor and ask to test listen to them. They might well accommodate you. You just can't appreciate the difference until you've done this for yourself. I can't speak for the Rode ntg but if it is in the same price range, it will probably deliver comparably. In audio, you really get what you pay for. A twice as expensive mic is actually twice as good.
In operation:
I always phantom power shotguns from an h6n. h4n is 2 AA vs. 4 AA for the h6n and dies quickly. There is a 2016 model h4n which has better preamps but I don't know about the battery situation. Don't buy an h4n from before this year, really subpar preamps compared to the h6n, particularly with a good mic. However, I run the h6n off of tenergy battery packs to eliminate this point of failure.
But this brings us to the heart of your question which is portability. I have always found it necessary to use shoulder rigs with all this stuff just to make DSLRs functional. When it comes to good audio outdoors, I find depending on anything less to be playing with fire quality-wise. It can be problematic when trying to use the new smaller gyro-gimbals. But then no onboard shotgun will work on those things anyway. (Mic might have to be mounted to the gyro on a bracket instead) Small Rig makes a line of high quality affordable rig gear.
In summation, with DSLRs you have to compromise somewhere. The choice is where to compromise:
1. A heavy bulky shoulder rig that is painful but allows for a top quality audio recorder, small battery pack and phantom powered superior mic for the best quality footage? However, very expensive. But you can always rent.
2. A small footprint lightweight hand held camera rig that lets you go anywhere fast but with a lesser mic recording to a lesser format inside the camera / an awkward DSLR-H6N-ME66 rig that always delivers ho hum audio and will fail you when put to the test in a bad sound environment.
Consider your shooting style:
What really matters is how far your mic is from your talent.
ME64 is a short shotgun so if you are more than a foot or two from your subject, you won't get good separation of their voice from the room or environment. ME66 is a little better but not much. Their voices will blend into the ambient noise and you will get reverb indoors. Now if you can always shoot within 1 or 2 feet of your subject, the difference between the ME mics and the others disappear. But is this realistic?
If you are 5 ft. away or more, these mics are not much better than your camera mic depending on the ambient noise levels. That is why the directionality of a 416 or the others is so important. Are you and your talent comfortable with you shooting from 2 to 3 ft. away to ensure clean audio? This is why critical work employs boom operators, handheld mics, lavaliers, or stand mounted mics for locked off shots. Proximity is critical to good audio quality. The cheaper or the shorter the shotgun range of the mic, the more quickly they fail as you move further away. So how close are you usually from your subject?
The Lavalier option:
While I always like to have a camera mounted shotgun, I use it as backup, and to make sure I have a good scratch track for audio syncing since it is seldom close enough to get quality audio. However, you might consider using Sanken Cos 11 lavalier mics coupled with Lectro, Sony, or Sennheiser transmitters and an h6n with receivers. You can wear a shoulder bag with the recorder/receivers in it and then headphone monitor. Then your camera is lightweight and you can move quickly if that is your style.
This is a very freeing option for a cameraman but unless you are using lectrosonic gear, wireless systems can really fall prey to bad RF interference. This is hit or miss.
Lectros are super expensive to buy and not cheap to rent. Sennheiser transmitters are more affordable. Sonys are in between price-wise but soundpeople I know think well of them.
Recommendation:
Sanken Cos 11 lavs for truly clean audio in any environment. Expensive to buy but cheap to rent. Combine it with a long shotgun like the 416, Sanken cS3 or Schoeps CMIT on a shoulder rig. Or get a boom operator so you don't have to worry about operating sound if possible.
I know the comfort of operating with all this stuff sucks and it will cost a LOT up front. If the quality of this particular work you are doing is more vital to you than comfort, you won't regret it. If you shoot a lot it will be worth it long term financially. If it isn't worth the expense and backache, go with the ME66, not the ME64 and get in as close as you can to your subject. Back it up with a lavalier if you can. H6n or 2016 h4n recorder is highly recommended.
Hope this helps. Good luck with your work!