What is the difference between cron.d (as in /etc/cron.d/) and crontab?

The differences are documented in detail in the cron(8) manpage in Debian. The main difference is that /etc/cron.d is populated with separate files, whereas crontab manages one file per user; it’s thus easier to manage the contents of /etc/cron.d using scripts (for automated installation and updates), and easier to manage crontab using an editor (for end users really).

Other important differences are that not all distributions support /etc/cron.d, and that the files in /etc/cron.d have to meet a certain number of requirements (beyond being valid cron jobs): they must be owned by root, and must conform to run-parts’ naming conventions (no dots, only letters, digits, underscores, and hyphens).

If you’re considering using /etc/cron.d, it’s usually worth considering one of /etc/cron.hourly, /etc/cron.daily, /etc/cron.weekly, or /etc/cron.monthly instead.

I would say the main difference is the obvious one: /etc/crontab and /etc/cron.d are not modifiable by regular users, while the per-user crontabs in /var/spool/cron that the crontab tool edits, are. (Subject to cron.allow and cron.deny, of course.) Of course on a system where you are the administrator, you could use either. On a shared system, the regular users can only use one.

Related to this is the extra field in the system-wide files, the username under which the job runs.