For H.264 and H.265 media, what bitrate and file size is as close to original quality as possible or the same as original?

I know that this is a non-answer, but the best thing to do is reencode a few files at multiple bitrates and see where the line is for you.

Try to get a few dark scenes, since that's where compression artifacts tent to be most noticeable.

Depends on the media. High motion live action is going to require a higher bit rate than low motion animation.

People really get confused when they see 50% reduction and exactly the same as X and think they'll just crank down the bitrate and be good. As others have said you really should try a few options although instead of bitrate you could try using crf values and find what works on your setup.

Also while screenshots can help, it really is something you should look at in motion. Sometimes you can think 'this looks horrible' but in motion it's fine and you never see it. But it also works the other way too.

There's a science and an art to getting good encodes. Hell even the encoders update and update little things behind the scenes that can effect the outcome as well.

I was wondering the same thing recently because my nvidia captures videos took like 1 TB of space on my main PC. I wanted to compress them by switching to H265. In FFMPEG there's no simple option like "loseless compression", you always have to enter manually the bitrate or quality. Rendering a bunch of videos with different bitrates and trying to compare them to see if there's a significant differene is a really long and annoying process. I gave up and just burnt everything to bluray instead.

Like others have said - it depends on the source media. In general, grainy sources require more bitrate to achieve a given quality as opposed to a clean, digitally shot source. You can choose a random bitrate and encode all your sources with it but you might not like the results or your encodes will be bloated for no reason.

Personally, having used both x264 and x265, I would stick with x264 for 1080p content. Yes there are some space saving advantages to using x265 but the time it takes really just isn't worth it - in my opinion. This is assuming you're using software encoding and not NVENC or QuickSync. Hardware encoding is much faster but yield larger file sizes and lower quality when compared to software encoding - again, not really worth it in my opinion.

This is very complicated to just give an answer, because:
It varies greatly based on the content. Animated compresses vastly differently than an action movie.

Varies greatly based on encoder. NEVC vs CPU etc

Varies greatly based on encoder options. I.e. -b:v -minrate -maxrate vs -rc vbr -qmin -qmaxcq values, etc

Varies greatly based on who is watching, the TV they use and their tolerance and experience.

Savings are greater at 4k than 1080p. But once you start adding HDR into the mix, you're in a whole new world.

Even the people with very discerning eyes can't agree on everything related to this topic. Wish I could just tell you do x... but you'll have to test various methods and determine what you are happy with.
or, if you just want some space savings... use some default setting that cuts it in 1/2 and forget about it.

18-21

If you really want original quality, you can just remux your discs. 1080p will already be H.264 and 4K will be H.265. I don’t really see a reason to re-encode if you’re going to end up with a 25GB 1080p video.

Interestingly, In starting to look into doing some re-encodes of some of my media to reduce disk space. Ran into an interesting one as I was doing some test files where the h265 file ended up being 30% bigger than the originating h264 (1.8GB to 2.4GB, Handbrake 1080p h265 fast RF 20). All my other test files were about a 50% reduction.

That is to say, there is no one singular set of settings that are perfect.

Encoding is an art. There is no perfect way to do it. For me, I just prefer remuxes because of that. Web DL should also be very similar for other media that doesn’t have physical options to remux from.

"Same as original" is not possible

How long is a piece of string?

I think you can safely remove about half the native bitrate and be perfectly within the range of "indiscernible". I don't like to think of H.265 as a means to use a lower bittrate. I like to use it to retain more quality at sensible rates. 25-30mbps is fine for most content, with a more prized movie getting a bit more overhead. Deleting non-used tracks and the likes is also a plus.

If you want constant quality, it's better to also encode using quality-based encoding instead of bitrate-based encoding. It allows rh encoder to save space where there's a non-complex scene and use more in more complex ones. It might, for example, be able to encode the few seconds of back screen at the begging of some movies in 50KB or something similarly small where bitrate-based encoding uses the full bitrate generating multiple MB.

This way you can easily get a 4K encode down to 4-8GB. Animation compresses incredibly well without percievable quality loss. Anything with grain will quickly balloon in size. Something like Star Trek (2009) with its insane amount of noise is more than twice that size if aiming for VMAF >95.

Why not go with a constant quality setting in the encoder instead of bitrate and filesize limitations?.

Thats what I do I feel CQ of 18 is indistiguishable from the original.

Bonus TIP when transcoding for static Use like storing and filesize reduction. always use a CPU never a GPU if you are after smallest filesize.