I need advice. My niece babysits her moms male dog time to time. He is neutered but they neutered him late (4-5 yrs old)

She wants to get a puppy and is not sure if a male would be better or a female. I guess the male still from time to time trys to jump objects

and she is afraid that if she gets a girl he will bother her, but could a later neuter be a cause for agressive behavior towards another male?
Please help
Thanks