4yo boys - personality clash, how to handle

[StormT]

Hi

We are relatively new to the area so trying to make new friends for DS, aged four and a half. Last year, I met a mum at the park with her similarly-aged son, the boys played nicely together and the mum and I made plans to meet up with them more often.
We've met up a fair few times, but not super regularly, but in the last few months, the boys don't play nicely together. We meet at the park, and they pretty much either ignore each other, or face off and argue about wanting to go on the same piece of equipment, both will want to hog it. If we go to their house or vice versa, neither child wants to share their toys with their guest.
I think they would like each other loads - they have lots in common, same kind of temperament, same energy. Perhaps that is the problem - too similar?
What should we do? I don't like being forced to be friends with someone I don't want to be with, so would extend the same courtesy to children, but I don't think it's that - the mum and I wonder if they are both a bit alpha-male and that's the issue - both stubborn and strong-willed.
How can we encourage them to be friendlier to one another, or should we give up for now, give them a break from each other and try in a few months? Or what?!

[MrsNextDoor]

I'd let it go OP....your DS will make his own friends in school...is he in preschool?

[StormT]

Thank you for the reply.

I was really hoping we could make it work.
DS is not in pre-school; we plan to home educate. We have a good group of home edded kids he mixes well with, and other friends too, but the mum of the boy in my OP and I both feel our boys could be such great little buddies, and I am not sure why they are behaving like this. I also feel we parents (inc husbands) connected, moreso than I have with other mothers in our new area. (I'm not doing nights out just the adults, I have a brand new newborn.)