I'm an American who's been to both places. I live in the southern US, where it is very humid. I can tell you that I was a little shocked at how humid Singapore is. It reminds of Florida. Your kids will adjust fine, but you and your wife will not really be used to the humidity. However, you will eventually adjust to it.
I like Singapore, but I have to tell you that you cannot possibly imagine how expensive it is until you go there. Unless you are a millionaire, you'll have to live in a government supplied flat/apartment. The cost to rent this apartment will be quite expensive. Want a car? Well, you have to buy a permit from the government first. This permit is only good for 10 years. Yes, that's right. After 10 years, your car must be returned to the government where I assume they scrap it. I have no idea if you get any compensation. This is in addition to actually paying for the car itself. I was told by a friend that the price for the permits is much cheaper now, but it still is an additional cost you must bear.
Schools teach in English with several hours a day devoted to "native language" instruction depending on your ethnicity. Your kids will be taught in English since you (presumably) are not Chinese, Malay or Indian. The quality of English in Singapore is excellent. If I was going to open a business somewhere and I needed really good English speakers, I would go there for sure.
Public transportation is excellent. Food is excellent too, with the major ethnic groups (Chinese, Malays and Indians) all contributing.
Singapore is, in reality, a one party political system. There are opposition parties, but the government does everything it can to prevent them from having any power. I could be wrong, but off the top of my head I think that only one member of an opposition party has ever won election to the Singapore parliament. There are no thought police in Singapore and the people are free, they just live in a one party system. Unlike some, I don't consider this to be a necessarily evil thing. The governing People's Action Party has done a lot of good for the country and honestly, not having to share power has enabled them to do things that turned Singapore into what it is today. I did not get the sense when I was there that the people felt that they were oppressed by the government or resented the lack of choice. What works in America is not necessarily the answer for Singapore and vice-versa. Many will not agree with me. All I can say is that I really do not have the impression that the average Singapore person sees himself/herself as an oppressed person with no political choice and the people who seem to be bothered the most by this issue are people who don't even live there.
Crime is low and while my Chinese friends don't really trust Muslims, Singapore does not at all seem to be a hotbed of Islamic fundamentalism. There was a plot some years ago to blow up US ships, but the government quickly stopped that. There have been no problems since then. There is no Islamic insurgency. The government takes a lot of pains to be sensitive to Muslim concerns and so far it seems to work. Illegal immigration isn't really a problem, unlike in Spain where the government cannot do enough to let illegals gain entry into the EU. Why the EU allows Spain to behave in this way is something I will never, ever understand.
I'm not sure about what vaccines you might need. Probably anything normal to a tropical country. Yellow fever and malaria aren't really problems as far as I know, but they are a little worried about dengue fever (even the US is starting to have problems with this).
I hope that helps you at least a little. Singapore is not a bad place at all, but it is expensive. Unless you get a gigantic raise for going there, I will be honest with you and tell you that your standard of living may go down from being in Spain. However, it's certainly possible that you might find the things that Singapore offers to somewhat compensate for that.