That depends what you're filling from & what to , on my AA510 it was 3 pumps per 2 shots, after first getting the pump up to pressure.
For the OP yes a pump is a bit cheaper & provided the air is dry it's fine but a cylinder is so much easier.
As for those Chinese compressors, by the time tax, shipping & import duty is paid the cost would cover filling a cylinder for best part of 10 years, & I doubt the compressor will last that long.