Here are three articles that talk about the two apps (1, 2, 3).
They are both spaced repetition systems, but here are some key differences:
- They have a different look and feel, so that is a subjective factor. Tinycards is more modern, while Anki is arguably starting to look dated.
- Tinycards decks are limited to only 150 cards. This is a problem if you like big decks. Anki decks have no practical size limit.
- Tinycards can connect directly to your Duolingo account and has shared decks (that the original owner still controls), but Anki has a lot of shared decks that instantly become "yours" (free to make changes) once you download them.
- Anki has more overall functionality, so if you like to add pictures and audio, etc, then you have more control.