Canned tomato paste is processed using citric acid rather than salt and has a slightly less robust flavor and thicker consistency. It can contain some off-tasting metallic notes.
Tubed tomato paste, on the other hand, is nearly always sourced from Italy, lending it a bit more uniformity in contrast to the can's wide-reaching nature.
The vessels impact longevity. You'll need to transfer paste from a can into an airtight container and place it in the freezer, since it'll spoil quicker in the fridge.
The tubed format can be kept in the fridge and used in small portions for a longer duration. However, this costs around twice as much, which is worth considering with frequent use.