The Spanish embassy in Wellington says they usually process regular Schengen applications within 15 days, sometimes extending to 30.
El plazo máximo para resolver los expedientes de solicitud de visado de corta duración (Schengen) es de 15 días naturales a partir de la fecha de presentación de la solicitud. Este plazo podrá ampliarse a un máximo de 30 días naturales en casos concretos
The deadline for resolving application files of short-term visa (Schengen) is 15 calendar days from the date of filing of the application. This period may be extended up to 30 calendar days in individual cases
The US page for New Zealand (presumably for Wellington) says they process nonimmigrant applications within 5-7 business days, but that's after the interview, for which there's currently a day waiting time.
Although visa processing time is typically five (5) to seven (7)
business days, processing time for specific cases may vary due to an
individual's circumstances and other special requirements, and this
may take a longer time. Visa processing cannot be expedited.
Note that while the US has its embassy in Wellington, that page for the interview wait times has times for Auckland. Also, these mean processing times also assume you have a complete and ready application.