Fix any integer $n$. Let $a$ and $b$ be two different integers such that $a+b \neq n$. Consider two vector bundles $E_{a,n-a} = \mathcal{O}(a)\oplus\mathcal{O}(n-a)$ and $E_{b,n-b} = \mathcal{O}(b)\oplus\mathcal{O}(n-b)$ over $\mathbb{CP}^1$.
Is $E_{a,n-a} \ncong E_{b,n-b}$ always true?
For example, $E_{0,-2} \ncong E_{-1,-1}$ since one has global sections while the other does not. By taking duals, we see that $E_{0,2} \ncong E_{1,1}$. What about $E_{0,0}$ and $E_{1,-1}$?
Yes, this is true. Without loss of generality, we may assume $a>b$, $a\geq n-a$, and $b\geq n-b$. Now tensor both sides by $\mathcal{O}(-a)$: we get that one side has sections, while the other does not.
In your specific example, after tensoring by $\mathcal{O}(-1)$, we have $E_{-1,-1}$ and $E_{0,-2}$, and the latter has global sections while the former does not.