For same bitrate which looks better between 720p and 1080p

[Sharc]

First off, the 1080p is encoded at a higher bitrate than the 720p (see media info for example), which makes it a slightly unfair comparison biased towards the 1080p.
Yet I find the 720p retained the details better, see for example the structure of the stones in the wall at the bottom of the picture, the needles of the pine, or the gravel on the very right. The 1080p smears the details more than the 720p for the "lowbitrate" encodes. I also found that the 1080p picture is slightly darker for whatever reason.
I am using AvsPmod for inspection, or any other player (e.g. MPC-HC) with which you can step through the frames. You should see the GOP pulsing at frame 50, 100, 150 etc. Watch the structure of the stones in the wall, for example.

At the end I would prefer your 720p over the 1080p in this "low bitrate" comparison.
Anyway, that's only how I see it.

[hello_hello]

Both JPEG screen grabs are 1080, the first of a 1080 video, the second of a 720 video. It's a good illustration of what a 1280 x 720 video will look like when played on a monitor or tv with 1920 x 1080 resolution.

No, it's simply an indication of what a 720p video will look like on a 1080p display when it's upscaled with a soft resizer, and maybe when it's also downscaled with a soft resizer in the first place.

Instead of jpegs, here are two identical clips. Both have the same grading and both have been rendered from the same original. One is at 1080p the other 720p.

I can't see the quality pumping Sharc refers to that easily in the original 1080p encode, but that's probably because the old PC I'm using at the moment doesn't have enough grunt to play it in real time (being 50fps). It's very obvious in the low bitrate version though.

For fun, attached are 4000kb/s re-encodes of your high bitrate 1080p sample. One at 1080p and another at 720p. The re-encode at 1080p doesn't look awful, even if it's not perfect, and the same applies to the 720p version. I did use quite slow encoder settings, which is somewhat natural when using a low bitrate, so attached is a second 720p encode using the default x264 settings. Comparing still frames from each shows the default settings didn't do as well where there's movement, and even the slower settings didn't encode the movement perfectly as it's quite a complex picture, but you'd probably have a hard time telling them apart while the video is playing.

That's an area where your samples aren't completely fair to the OP's situation. You've used a very complex picture in a very short sample. There's much less opportunity for a decent encoder to distribute the bits sensibly and keep the quality high compared to encoding an entire movie at the same bitrate. 4000kb/s is only the average.

I also ran a single pass 720p encode using my usual x264 quality setting of CRF18, and it came in at around 7400kb/s, but I did expect it to be higher as the CRF method seems to throw more bits at the first frame when it contains a complex picture (the quality of P and B frames are dependant on the quality of the I-Frames they reference), so for a very short encode the bitrate naturally ends up higher than it often would be when encoding a complete video.

I won't deny when pausing the picture on individual frames I can see a slight loss of detail in some frames for the 720p versions. Mostly looking at the wire fence and chain as they're not as sharp, but that doesn't mean everything else in the picture looks the same way, or that it'd be something a mortal would notice at normal viewing distance, and I suspect you chose a 1080p sample with the most detail you could find, which wouldn't make it typical. Also attached are two screenshots of the 720p encode upscaled to 1080p by MPC-HC, one using softer upscaling than the other so you know how they look to me. They're both upscales of the same 720p frame, so the difference is simply the upscaling method.

[ChapmanDolly]

Well, at the end of the day it comes down to personal preference, so I'm going to stick with 1080p. If you feel like experimenting further, here is the original camera file, only chosen because it was handy and not for the detail content.

[Sharc]

…., so I'm going to stick with 1080p.

Yes, as long as you keep the bitrate high enough it's fine, but rather not for 4Mbps with your encoder (Low bitrate 1080p) I would say. There might be a better setting for the encoder though; I am not familiar with DaVinci)

[hello_hello]

For funzies, encoded using the x264 settings I'd typically use, at the minimum quality (CRF value) I'd typically use for each resolution, and encoded at 25fps, given it's a more typical frame rate for movies. 900p is included as it's a compromise I sometimes use when downscaling to 720p does reduce detail, but 1080p is still more resolution than required.

720p - 8237 kb/s
900p - 10.8 Mb/s
1080p - 19.5 Mb/s