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In addition to what Andy said, the DC servo method doesn't add impedance to the signal.  Note that in your bottom circuit, the signal with the DC offset removed has an impedance of 1 MΩ at DC.

In your case it doesn't matter since the signal is only going into an opamp input.  In other cases it might force the use of a buffer, or some other means of dealing with high impedance, when that would not otherwise be necessary.  For example, if you didn't need that additional gain after the offset removal, it might be inconvenient to have the signal be high impedance.