Step 1: Analyze Statement I.
Among the elements \(N\), \(P\), \(As\) and \(Sb\):
\[
\text{Electronegativity order: } N>P>As>Sb.
\]
Thus, \(X = N\) (most electronegative) and \(Y = Sb\) (least electronegative).
The oxide \(N_2O_3\) is acidic in nature, while \(Sb_2O_3\) is amphoteric.
Hence, Statement I is true.
Step 2: Analyze Statement II.
Although \(BCl_3\) is covalent and undergoes hydrolysis in water, it does not produce both \([B(OH)_4]^-\) and \([B(H_2O)_6]^{3+}\).
The ion \([B(H_2O)_6]^{3+}\) is characteristic of \(Al^{3+}\), not boron.
Thus, Statement II is false.
Final Answer:
\[
\boxed{\text{Statement I is true but Statement II is false}}
\]