The A/R has a marked effect on the turbine side, but not a lot of effect on the compressor side.
So just referring to the turbine end:
The smaller the A/R the faster the spool, but a corresponding reduction in shaft torque. So if your A/R is too small the turbine will struggle to drive the compressor at the desirable flow&pressure, especially as you rise through the engine rpm.
So while A/R affects the pressure differential, the trim affects the operating range. Maintaining the same trim, but increasing the turbine diameter will increase the imparted shaft torque, but it will move the operating range up the rpms and introduce more lag. If you increase the trim value by increasing the minor (inducer) you will also make it more laggy, but effectively shift the compressor map to the right (biased to the surge region). If you decrease the minor you will effectively shift the map to left (biased to the choke region) and with it the pressure will build faster and at a higher pressure for the same compressor mass flow rate.
You select the A/R based on what exhaust manifold pressure you want in relation to the boost pressure. Compressor trim tends to hover around 72% of the turbine trim for reliable street use..