I've been struggling to find the difference between those two structures, is
one of them wrong or they are both right and have a difference in
meaning/emphasis

> 俺が走るのが見た

> 俺が走るのを見た
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question
grammar meaning nuances particles transitivity
About the difference in these sentences with のを and のが
の is a nominalizer, が is a subject marker, を is an object marker, and 見る is a
plain transitive verb meaning "to see". 俺が走るのが見た is plain wrong because the
act of running cannot see something.

  * ❌ 俺が走るの **が** 見た。(incorrect)  
❌ My running saw [something].

  * 俺が走るの **を** 見た。(correct)  
[Someone] saw me running.

However, there is another verb 見える which means "to be visible", "to be in
sight", "can be seen". This can take an action as a subject. See: [What is the
difference between 見る and
見える?](https://japanese.stackexchange.com/q/39242/5010)

  * 俺が走るの **が** 見えた。(correct)  
[People] could see me running. / My run was visible.
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answer
You shouldn't view your sentence as

> 俺が走る + のを + 見た

Rather, it is

> 俺が走るの + を + 見た

From there, it is easily to see that の is just the 代名詞 that makes 走る(to run)
into a noun 走るの(the action of running). The が and を are just being used
normally here, and your sentence should be interpreted as such:

> 俺が走るの(The action of me running) を 見た(saw)。  
>  (Someone) saw me running.

Obviously, "running" isn't a person and thus cannot see, 俺が走るのが見た wouldn't
make any sense here. ("The action of me running saw???" What could an "action"
see?)

P.S. you could, however, say 俺が走るのは見た. は does not specify it's the subject or
object, but obviously it changes the emphasis(and thus the meaning to some
extent) of the sentence by now making 俺が走るの the topic.
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answer