Just a note, "Visual Complex Analysis" is a terrible book to learn complex analysis. Proofs are very iffy, akin to sketches of proofs. With that said, it is a excellent supplement to another std. complex analysis textbook.
Is it just the normal difference between e.g. an engineer's approach to real analysis and a mathematicians (but complex analysis swapped in), or something else?
I can think of a lot of fields where a decent grasp of complex analysis concepts would be very helpful even without being able to do rigorous proofs.
I can think of a lot of fields where a decent grasp of complex analysis concepts would be very helpful even without being able to do rigorous proofs.