This thread is full of people who don't know what they're talking about.
First of all, let's clarify some terminology as people are misusing mnemonic and seed. A mnemonic is something that is completely different from a seed. A mnemonic is any way to encode a sequence of bits (aka a number) as a sequence of words. A seed is very specifically defined by
BIP 32 as being a "byte sequence S of a chosen length (between 128 and 512 bits; 256 bits is advised) from a (P)RNG)." A mnemonic can be used to encode a seed or be used to produce a seed. BIP 32 also specifies how to go from the seed to the master private key via hashing. Because it is hashed, you cannot go from an xprv to the seed.
Both Electrum's mnemonics (which they confusingly call seeds but are not actually BIP 32 seeds) and BIP 39 are specifications for
mnemonics and how to go from some initial entropy to a mnemonic, and from the mnemonic to a seed. Specifically, both specify that the BIP 32 seed is produced by hashing the mnemonic using SHA512. Because the seed is produced by hashing, you cannot go from a known 512 bit seed to a BIP 39 mnemonic or an Electrum mnemonic because hashing is a one way function.
Bitcoin Core does not use mnemonics. It does have a BIP 32 seed, but this seed is 256 bits in length is not produced as the result of hashing or of a mnemonic. This seed is used to generate the master private key which is then used to derive the child private keys that are actually used. This seed is never shown to the user, and for the most part, users really don't know that this seed even exists.
The only way to get Bitcoin Core's seed or the corresponding master private key is to use the
dumpwallet command and find them in the wallet dump. Once you have the seed, you can import it into another Bitcoin Core wallet using the
sethdseed command, thereby restoring your wallet from the seed.
But you would not be able to use this seed in any other wallet software. You cannot go from a seed to either a BIP 39 or Electrum mnemonic, so you can't get some mnemonic that could be imported to some other wallet software. And for importing the seed by itself, I don't think any other wallet software will let you do that.
As for the master private key, it is absolutely and utterly useless for backup and restore scenarios. You absolutely should not backup that as you will find that it will be difficult for you to recover your Bitcoin. Bitcoin Core does not allow you to import master private keys so you would not be able to import it into another Bitcoin Core wallet to restore your wallet. You could import it into another wallet software, but Bitcoin Core does not use the standard derivation paths used by other software nor does it use different derivation paths for different address types as most other wallet software do. So what you will find is that whatever wallet you use probably won't be able to derive the keys that you are actually using due to the nonstandard derivation path. If you are able to derive the keys, you probably won't see all of your addresses unless your wallet will generate all of the address types for a given key, which I don't think any other wallet software does. So in general, the master private key really isn't going to be useful and is just going to be painful to try to restore from.
Now you could still save the seed and do
sethdseed as I mentioned above. But the seed would only be useable in Bitcoin Core, and it would be formatted like any other WIF private key. You'll need to store and write down that seed somewhere and know that it is a seed for Bitcoin Core and not just some random private key. You probably won't be able to memorize it like a mnemonic so you need to save it somewhere. You could encode it as a mnemonic using some other software, but you will need to know how it was encoded as a mnemonic, be sure that you don't mistake that mnemonic for a BIP 39 or Electrum mnemonic, and be sure that the mnemonic is invertible. Furthermore, by using some other software, you are exposing your seed to another potential attack vector. So in general, storing your seed is going to still be more complicated than just a mnemonic and you still have special considerations for it. It will probably be easier to just store your seed as a digital file.
But at that point, you might as well just store the wallet.dat file. This is by far the easiest backup method. You won't lose your seed, and if your seed has changed (which it will when you encrypt your wallet), you will still have that. You'll also have your transactions, transaction metadata, and address labels backed up which just storing your seed cannot do. And a wallet.dat is unambiguously for Bitcoin Core so you know exactly where to restore your wallet.dat file and be able to get restored way faster than any other method which would require rescanning. So I would instead recommend that you backup your wallet.dat in multiple places instead of your seed or master private key.
tl;dr backing up your seed or master private key and then trying to restore from them is way more difficult and introduces more room for error than just backing up the wallet.dat file. Just backup your wallet.dat file and you'll be far better off.
