In terms of convenience, Electrum wins Core with no questions. Electrum allows the user to export the keys and to store a physical copy of the seeds thus giving them the reliability of physical backups. It's not possible with wallet.dat.
While it is inconvenient to do, it is possible to get the seed value (not a mnemonic, which many people, including you, confuse for being the seed) from Bitcoin Core and back that up. The seed value can be gotten using the
dumpwallet command and the seed value will be there in WIF format. You can use that with
sethdseed to restore the seed value to a new wallet.
In terms of security, Core would win. Core allows the user to encrypt their wallet and thus giving them a better security.
You can encrypt Electrum wallets too.
While Core allows the user to export its HD key, the wallet still has to be backed-up relatively frequently whenever the password is changed. It does seem more of a hassle to manage the wallet.dat.
That is untrue. The seed does not change when the password is changed. It is only changed when the wallet is first encrypted.
Which are the security differences comparing the Electrum HD wallet which has an exportable seed to the HD wallet.dat from Bitcoin Core software?
Besides the seed, there are other security concerns with the derivation of private keys themselves. Electrum uses a derivation path with non-hardened derivation nodes since it follows BIP 44. There is an inherent security risk to this because it is possible to retrieve the private key of the parent of a non-hardened node if you have the private key of that non-hardened node, and the extended public key (xpub) of the parent. With hardened derivation, this is not possible. Bitcoin Core uses exclusively hardened derivation paths. Unfortunately this makes public derivation impossible so it is more annoying to use as you have to import addresses to watch.
I would trust Bitcoin Core more in general.