Hello and thanks for the question.  The answer will depend on what type of tiered container you are talking about.  If it is the ‘strawberry pot’ that is sold most places, there really isn’t much of an advantage for that—in my humble opinion.  They are very small, and you will need new plants every year.  They do look cute though.  Strawberries in raised beds are a different thing.  Raised beds are easy on our backs, they are larger and the strawberries can be kept year to year.  Only plant 4 plants per one square foot though.  Also make sure any runners that go over the edge are cut back for the health of the mother plant.  There is no place for baby to dig into the soil and get nutrients.  Here is a wonderful article from Oregon State—the other OSU.  https://catalog.extension.oregonstate.edu/sites/catalog/files/project/pdf/ec1307.pdf

Hello again,

While that is a very cute planter, you will still be having to change the soil seasonally.  Changing the soil, also includes changing the plants.  If you are willing to treat your strawberry plants as annuals instead of perennials, as some people do with mums, then there are no problems. Being tiered and not deep or wide in any spot will mean that it dries out easier and will require very frequent watering.   If space is tight for you, I would suggest a raised bed planter (helpful for your back) even one of the same size, 5 square feet and using a good garden soil, that you can amend like you do your in ground soil yearly.  That way you will not have to change the soil.  The larger I separated planter will be more beneficial for the plants.  https://www.gardeners.com/how-to/raised-bed-buying-guide/9564.html

See the picture in the back left corner for an idea of the planter