voltage - Are cutoff frequencies of bandpass and bandstop filters equal?

Consider the two filter in picture

^{simulate this circuit – Schematic created using CircuitLab}

Are the cutoff frequencies (i.e. the two frequencies at which \$V_{out}=\frac{1}{\sqrt{2}} V_{in}\$) the same for the two filters? (And therefore also the bandwidth is the same for the two filters?)

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I think they should be the same since in both cases the condition \$V_{out}=\frac{1}{\sqrt{2}} V_{in}\$ reduces to

$$R^2=(\omega L-\frac{1}{\omega C})^2$$

Nevetheless it is strange that there is a frequency for which both \$V_{out}\$s taken at resistor and at LC series have the same value \$\frac{1}{\sqrt{2}} V_{in}\$.

Doesn't this violates Kirckoff voltage law? (At any time it should be \$V_{in}=V_{R}+V_{LC\ series}\$ but if \$V_{R}=V_{LC\ series}=\frac{1}{\sqrt{2}} V_{in}\$ then this is not true).