Do switched capacitor integrators have lower drift?
What's great about switched capacitor (SC) is that, when properly configured, they allow the effect of a variable resistance when driven with a variable clock rate. Which is good for things you want to tune. If you're an IC manufacturer, it's a powerful technique to produce interesting on-chip functions.

What's bad about SC is that no switch is perfect, charge injection from the clock into the output node can introduce an uncertainty into the design not present when using simpler components.

To complete an integrator, you need an amplifier, which will have offset voltage, bias and offset currents, and variations of those with temperature and time, regardless of whether currents are being controlled by resistors or SC.

In summary, there's no reason a SC design, especially one built from discrete components, should be any better than an equivalent resistor one, and in fact reasons it should be worse.

An SC one could be made better if you can take advantage of the new topologies the concept of a flying capacitor could allow. A flying capacitor can move charge from one voltage to another with minimal (not zero) influence of the voltage. While this is similar to what a cascode stage would allow you in a conventional design, it's much more flexible, and can allow you to sum currents directly and eliminate some amplifiers.