What are the criteria to be applied when choosing the instrument for C-V measurements from the 4294A and E4980A?

It depends on the size and the thickness of the gate oxide film of the device. Generally, for the semiconductor devices at 90 nm node or less than 90 nm node, it is important to improve the measurement accuracy by increasing the frequency (typically up to 10 MHz range) and to characterize the device with an equivalent circuit model in which a conductance for leakage tunneling current flow through thin gate is incorporated. To perform C-V measurements in the high frequency range and to automatically derive the capacitance based on the sophisticated equivalent circuit model, it is recommended to use the 4294A. Refer to Paragraph 7 on page 18 and 19 of Application Note 4294-3 for the details of measurement technique and equivalent circuit analysis algorithm. For the semiconductor devices in excess of 90 nm node, generally the E4980A is recommended because conventional spot-frequency or multi-frequency C-V measurement up to 1 MHz can be used.