There really is no way to know without more information. Here is why:
Portfolio 1: Expected was 1%, Realized is 2% (1 percentage point higher) +2 Beta Security: Expected is 2% (2x the expected return of the first portfolio)
Portfolio 1: Expected was 10%, Realized is 11% +2 Beta Security: Expected is 20%
Clearly in order to solve this you need to know more. In the first example the realized and expected returns are identical. In the second example, however, the expected return of the +2 Beta security is closer to double what the realized return of the portfolio was.
If I'm interpreting your question correctly: A security with a beta of 2.0 is expected to gain twice as much as the market in an up market and lose twice as much as the market in a market decline. It's theoretically twice as volatile as the S&P 500. A security with a beta of 1 or 1% greater would theoretically be less volatile than the 2.0 security and provide a lower return.
Besides the previous comments, there is an assumption made that the two securities' returns are highly correlated with each other. If they are not, it is not statistically correct to depend on beta as a risk measure.