It is usually said that opamps are used for resistive loads and OTAs for capactive loads...

Why is that so...?

Another way to look at it: OTA is an Operational Transconductance Amplifier which means it converts voltage to current. Therefore, the output port is ideally a voltage controlled current source. Now, in a real circuit, there is some output impedance in parallel with that current source, the resistive part of which should be very big so that the DC gain is very large. We need this large output resistance so that the output port of the OTA can be approximated with an ideal current source. If you connect a small resistive load (compared to the output resistance) to an OTA, its DC gain drops. An OpAmp is basically an OTA followed by a driver stage, like a source follower, which reduces the output resistance and can drive small loads.