I think going from 1 to 2 is harder. Going from 0 to 1 was hard, and threw everything for a loop, but it was just me and my husband that were affected and we could talk about everything and sort it out in about 2 weeks - that was when we felt like we were getting to our new "normal".
When our second was born, our older one was 2.5. Like a previous poster said, we also have no family near us for help, and most of our friends live about 30 min. away. I think the thing that was actually hardest for us was dealing with how it changed our family dynamic. I stay at home with the kids while my husband works, so I spent every single day with our oldest. It was very very tough for me to lose that one on one time with her. When we got back from the hospital, she seemed like a giant, and seemed to have gotten so much older than when we left her (it had only been 2 days!). Those feelings of loss have started to dissipate now that we're getting another new "normal", and the baby is starting to really be a part of playing and interacting.
But, now that that is starting to settle, I'm struggling with the logistics of having two kids! Some days are so much fun and are so smooth, and sometimes I'm constantly having to make the choice of who needs me more between two crying, very upset kids! It's tough! And the baby really doesn't nap well in the stroller or the ergo, so it feels like we can't go do anything outside which isn't so fair to our 3 year old. It stinks when it feels like either way, someone is going to always have to lose out. Our daughter is exceptionally understanding, and loves her brother like crazy, so that definitely helps though.
The last thing is similar to what another poster said - my free time is GONE! By the time I finish reading to my daughter at bedtime, my son usually wakes up (he won't take a bottle!), and when I'm done there, it's practically time to sleep because our son still wakes up so much. So there's very little time that I get to spend with my husband, just us alone. Which was very hard in the beginning when we were both so emotional about the changes, but couldn't really talk much while our daughter was awake (talking about the changes with her was very helpful for her, but seeing her mother a blubbering mess would be very scary to a 3 year old!), so everything had to wait until night, and by then we were exhausted!
So I'd say the first few months of 1 to 2 is exceptionally hard - harder than 0 to 1 (for us, anyway).