What's your rationale for saying the other series is better?
After edit: yes, I am aware there are a few different textbook series under the title "Primary Mathematics" from Singapore publishers, but I haven't noted any significant differences among them. I still use the old third edition Primary Mathematics series adopted in Singapore rather than the new United States edition, for example.
It's been a while since I researched it, so don't remember fully.
One problem was figuring out which version of singapore math to get (for example the new one in singapore is not considered as good).
A bigger problem was that it doesn't meet state standards (I was researching for a school) and MCP does - while still being very good. (BTW they ended up using Addison Wesley grrr.)
Also an issue that some raised was the cultural differences that might show up. (Not a big issue, but why add obstacles?)
I think there was some issues raised that singapore math is not as flexible in dealing with students that have have varying learning styles, while MCP did a better job of that.
To a homeschooler this might not matter though.
But MCP really is very good and has none of those drawbacks. (I also looked at Saxon math, but it had WAY too much drill.)
Also, this is more of a "soft" reason, but a lot of reviews seemed to like it because it was from a different country. "They do well in school, so it must be the book." But I think cultural emphasis has a larger role than the book. There seems to be a lot of self-hate by homeschoolers - they don't like the schools, so they don't like anything american, therefor anything imported must be good.
I know none of this really gives a good answer for you. I had to pick something and MCP just seemed better.
After edit: yes, I am aware there are a few different textbook series under the title "Primary Mathematics" from Singapore publishers, but I haven't noted any significant differences among them. I still use the old third edition Primary Mathematics series adopted in Singapore rather than the new United States edition, for example.