Here, *"our"* is a determiner, and specifically a definite determiner, while *"more powerful than your computer"* is a restrictive clause. In other words, *"more powerful than your computer"* tells you ***which*** smartphones we're checking Facebook on. If you put *"our"* in the sentence as well, you've already said which smartphones we're checking Facebook on, so you need to use a non-restrictive clause. You can do that by inserting *"that/which are"*.

Consider.

> I check Facebook three times on the way to work on a smartphone more powerful than your computer.

Here *"a"* is an indefinite determiner, so this works fine.

> *I check Facebook three times on the way to work on this smartphone more powerful than your computer.

And *"this"* is a definite determiner, so it sounds wrong.

UPDATE: In the comments, Edwin Ashworth points out that it's not the fact that *"our"* is a definite determiner that makes this sentence ungrammatical. It's the fact that *"our smartphones"* has already completely determined what we are referring to, so we can't use a restrictive clause to narrow it any further.