How secure is it to upgrade bitcoind? The release notes of bitcoin-core suggest to just copy the bitcoind file, which appears on my system (Raspbian Butch) in /usr/local/bin.

Since I built from source using ./configure I wonder how this will influence my node. Is bitcoind really the only thing that gets changed with a new release?
Although certain releases perform database upgrades, the upgrade is handled by the bitcoind binary - updating a node only requires changing the binary, regardless of whether you downloaded a prebuilt one or compiled it from source.

If any additional changes to the bitcoin data are required, the updated bitcoind will perform them when it starts.

If you are downloading a prebuilt binary, make sure you get it from a reliable source (such as bitcoin.org) and verify the signatures to make sure it has not been tampered with.