Is the electric field the same along any equipotential line?

No. An equipotential line is described by a scalar voltage (volts). Electric fields are a vector (volts per meter in a particular direction)

For point sources, or uniform charge distributions in constant, uniform permittivity spaces, the E-field is usually proportional to the equipotential voltages.

But for space where the permittivity changes (e.g. at the edge of a capacitor; from a capacitor dielectric to the surrounding air), you can map the equipotential lines, but the volts per meter (E-field) will change -- the 'volts' of the equipotential line will not match the 'volts' of the E-field. This is because the 'distance' and direction changes for the vector.