Ds2 was 4wks prem, he pretty much just slept & fed until his due time, then he started to be awake for short periods like any newborn. He's just 6m now and no different from his full term little friends.
Mine was born at 32w and home at 35w. He is now 38w and still mainly sleeps, feeds, sleeps. He slept for 6 hours flat last week! But that was the calm before a 6weeks growth spurt at weekend where he barely slept at all.
He's only really awake and looking around for half hour or so during breakfast (lets me and 2DCs have breakfast in peace).