To Neuter or not to Neuter?

Our Ernie has just passed 18 months, so is at the age where the vet recommended castration. I have him booked in at the end of this month, and I'm still in two minds as to whether he should lose his love eggs but my Wife 100% wants him done.

He has a brilliant temperament, we have two young boys and he's pretty good with both of them.
He's friendly with all other dogs, even in the face of an aggressive one it doesn't seem to affect him.

The only negatives - and in my opinion, they're pretty big ones...
Recall - he will respond to me but not my Wife, and he has a tendency if he picks up a scent to race off at 100mph. He recently did this at a national trust site and we found him 1/2 a mile away sniffing some poor couples' cocker spaniel. Thankfully they were fine with it but many aren't.
He's also strong puller on the lead - or was until we started using a halty (he's like a completely different dog with it on), and he marks until he is completely empty and then does some phantom marking still.

Questions/opinions then, will neutering help with any of the above issues? Asking those that have been/experienced similar.