I have two DDs and 3 years. I had wanted 2 years, but we ended up going for 3. For us it is perfect.
My eldest had her own babyhood (the eldest is forced to grow up when the second is born) was out of nappies, going to preschool, able to help, able to understand when DD2 was born. It wasn't difficult having DD2, because by that stage,DD1 slept, understood sometimes she needed to wait, could take herself to the toilet etc etc..
As for closeness, yes they are very close. They choose to play together at school, share friends and get on really well. But, I think how close children are is more down to personality than age. I have a friend with children not much more than a year or so apart. Despite being the same gender, they hate each other, I mean really hate as in they cannot be left alone together. My children share interests and hobbies, so they're very similar and have compatible personalities (ones a leader, one likes to follow). They're downstairs playing together right now. When at home, they play together all the time. I think though, that's just the luck of gender and temperament more than anything else.