A traumatic labour can have a big impact on a baby (and mum of course) to what extent it affects their personality long term I don't know, I can imagine it could have an impact on them in the short term. Both my boys were born very quickly, stress free and pain free births, I've only been in labour for a total of 5 hours in my life with both boys, neither were very good sleepers, they both BF fine though, both were content babies but in terms of personalities I would say they're different.
I think what has a bigger impact is what order a child is born, I think older children generally tend to be higher strung because they're used to being centre of attention, by the time we have our second child we're much more relaxed, don't fret as much as we do first time and we probably continue to parent this way, so I think this is more likely to affect their personality long term than something like labour. Most younger children I know (as children and adults) seem much more chilled out people, I can quite often tell if someone is an older or younger child lol, but of course everyone is different it won't be like that for everyone.