Step 1: Understanding the Concept:
Acidic, neutral and basic solutions are told apart by comparing \([\text{H}_3\text{O}^+]\) with \([\text{OH}^-]\).
Step 2: Check statement (A).
\([\text{H}_3\text{O}^+] = [\text{OH}^-]\) describes a neutral solution, such as pure water at 25 degrees C. So (A) is FALSE.
Step 3: Check statement (B).
In a basic solution \([\text{OH}^-] > [\text{H}_3\text{O}^+]\), so excess hydroxide ions are present. So (B) is TRUE.
Step 4: Check statement (C).
Excess \(\text{H}_3\text{O}^+\) is the definition of an acidic solution. So (C) is FALSE.
Step 5: Check statement (D).
The correct relation is \(\text{pOH} = -\log[\text{OH}^-]\). The expression \(-\log[\text{H}^+]\) is pH, not pOH. So (D) is FALSE.
Final Answer:
Only statement (B) is correct for a basic solution.
\[ \boxed{\text{(B)}} \]