There's roughly 2yrs between my two - and my eldest started getting night terrors from about 2yrs - which lasted until she was over 4yrs old. So for a couple of years, sleep wasn't great. Eldest would have terrible screaming episodes in the middle of the night It went in phases - sometimes it would be once a week, sometimes it would be several nights a week, then there'd be a few weeks of peace, but then it would come back again. The terrors could just be a single shout-out, to several horrific screaming episodes a night. How we never had the police or Social Services round I'll never know!
Luckily, our youngest was a wonderful sleeper, dropped off quickly and easily from day one, slept almost continuously apart from changes/feeds for the first two months, and even slept through eldest's night screaming (In the same room. Quite a feat.). It's true that one child can be completely different to the next - even today (they're now 3 and 5) - youngest goes out like a light, whilst eldest tosses and turns - though she has grown out of the night terrors.
The other tricky period as I recall was potty training eldest whilst youngest was still on the boob, so there were times at soft play etc, that I'd be in the middle of feeding youngest, when eldest suddenly needed to 'go' - which were a bit of a juggle and could be stressy. But that didn't last very long.
I'll be honest and say sometimes it was awful, and incredibly stressful and a strain on myself and DP's relationship. But because it wasn't at the same constant level all the time, it was 'OK'. Somehow we just got through because the next day could be fine etc. Also I think the second baby for a lot of people is much easier, because you've sort of been there before, and are just more relaxed. I found that my youngest just slotted in really easily.
I love having the two of them so much! They're brilliant companions for each other, and I actually found a 'secret' note by the eldest the other night, which said "I love my little sisder [sic]" that made me go "Awwwww..." The lack of sleep in the early days is more than made up for now. We can also have longer lie-ins again, because they have each other for company and entertainment. They just chat and play by themselves, while we get an extra hr or so in bed!