Delta bots always need all motors to step to maintain a straight level. Microstepping, is not magic, the incremental torque decreases per step so that you will be more likely to miss a few micro-steps. Furthermore, the signal that creates voltages for the micro-step positioning is usually not perfectly sinusoidal (pulse-width voltage modulation is used to achieve micro-stepping by controlling the current; the driver sends two voltage sine waves, 90 degrees out of phase to the motor windings), micro-stepping drives can only approximate a true sine wave. This means that some torque ripples, resonance, and noise remains and hence resulting in odd stepper behavior, like seen below from this ref. (after the half step the stepper jumps to the full step and maintains that value for a while):
This is seen as a Moiré pattern in your printed products. As an example, if the head is moved in Z direction by micro-step, you will almost certainly notice that the head doesn't move on every micro-step, but only every 3rd or 4th micro-step (as an example). When using higher resolution steppers like the 0.9° stepper motors, you will still miss micro-steps (e.g. the same, so also on every 3rd or 4th micro-step the head moves), but as the micro-step is half the size of that one of a 1.8° stepper motor, the accuracy as in precision and resolution is higher.
In that sense, if you change your stepper drivers for higher micro-stepping drivers (from 1/16 to 1/32 as you mention), it will not help you improve the resolution much because the incremental torque from one to another 1/32 micro-step is lower than for 1/16 micro-steps as can be seen in the figure below (taken from this ref.).
So, using 0.9° motors (and keeping 1/16 micro-stepping) improves positioning accuracy as described above, it will also reduces the noise, because the torque per unit angular error is nearly doubled. Also remember that if you are using 8-bit electronics (you hint to an ATMega board), then even 1/32 micro-stepping burdens the processor to achieve reasonable travel speeds. With 8-bit electronics, it is usually suggested to use 1/16 stepping.
Upgrading an existing printer from 1.8° to 0.9° stepper motors is probably not worth for the majority of users (note that the maximum allowable speed also reduces when using 0.9° stepper motors). Unless you are designing and building a new delta, or aren't on a tight budget you could opt for the additional costs of buying 0.9° stepper motors.
Note that updating to higher micro-stepping values not necessarily implies that the quality of your products also increase. See e.g. this reference.