Well injury wise, spring free tramps are most likely safer simply beacuse you dont go as high. I had a tramp with straps instead of spring for three years and it sucked but there were no injuries at all. This summer I convinced my parents to buy a sick rectangular tramp with springs and within a month one kid broke his knee and my bro broke his foot.
Bottom line is it depends what type of non-spring tramp you get, but its not the springs that are going to injure you, its the way you land and the height that that tramp send you that is going to cause you to land awkward and hurt yourself
;){kind=link}