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As far as Electrum goes, from what I've read, I cannot trust the whole "your wallet can be spawned with a seed" setup. Im too paranoid with the idea that the right combination of words can spawn your entire wallet. It's a bit fucked up actually.
well your bitcoin core wallet is also an HD wallet meaning it is "spawning" all your keypairs from a seed, it just doesn't give you any mnemonic!
as for your paranoia, it all comes down to that random entropy the wallets are using. if it is good enough then the "combination of words" you see is showing that random entropy to you in a human readable form that you could write down.
pooya87 is right.
All (proper) walllets use the same mechanism. They use one seed (not mnemonic, but seed) which has been generated with a good amount of entropy (usually 256 bit) to derive all private keys.
Some wallets (the majority, excluding bitcoin core) do
encode this seed via BIP39 which then gives you the human-readable mnemonic code composed of 12 / 24 words.
In the end, it is all the same. Just the depiction of the big random number (seed) differs.
Security-wise it doesn't matter how you encode the seed. All that matters is the entropy used to generate it.