In reply to top cat:
Sorry but thats just not true. I always found sport climbing far scarier than trad (for reference this was the case until a couple of years ago, when my max trad onsights were e5 and max sport redpoints 7a+/7b) which i basically put down to the fact that you spend a lot more time on the edge of falling off when sport climbing. The only way I could get my head round this was to tactically go through the motions of learning to fall IE - small controlled falls at the wall, bigger controlled falls, falls whilst climbing and then finally falls whilst clipping when pumped. I couldn't care less about falling whilst sport climbing now (when it is genuinely objectively safe to do so) but it takes continued fall practice to maintain this attitude. After a long hiatus it takes a while to build such confidence again. Such confidence has allowed me to push my sport grade considerably, which has made me far more confident on trad routes due to being used to doing harder moves.
All of this, and I've never been particularly scared of falling on trad (when objectively safe of course). Perhaps because its a lot slower and more measured, with constant risk assessment and reduction, whereas sport climbing youre 100% going for it.
I think the important thing is to recognise that most of the time falling IS objectively safe, and to learn to recognise when it is from when it isnt. Being a confident sport climber DEFINITELY helps with that.
Edit - of course, having an experienced belayer that you trust an other such details should not be overlooked.
Post edited at 15:40