To compare the fractions, let's convert them to a common denominator or simply convert them to decimal form.
\[
\frac{1}{4} = 0.25 \quad \text{and} \quad \frac{4}{3} = 1.3333
\]
Clearly, \( \frac{4}{3} \) is greater than \( \frac{1}{4} \), so the bigger fraction is \( \frac{4}{3} \).