Interesting question. I came across Aerial observation; the airplane observer, the balloon observer, and the army corps pilot, copyright 1921 and written by Harold E Porter, Formerly Captain, Air Service, United States Army. I scanned the book for "danger" (I understand that this is now the academically respectable technique of "remote reading", not to be confused with the egregious sin of "not reading your sources"). Unfortunately the book seemed rather inconsistent, and gave no statistics. I found the following quotations interesting.
Sir David Henderson, testifying in the R. F. C. inquiry of 1916, declared that the least dangerous of all aerial work is fighting in a fighting machine; and perhaps this is sound, for the Observer's peril is certainly greater, and there are not many more kinds of aerial work, anyway. The chasse Pilot has a few short, sharp actions, and is through for the day; the Observer and the army corps Pilot fly for hours at a time, frequently under continuous fire from the ground, and always the attacked, and never the attacking party in a fight. Certainly the figures show that fewer chasse Pilots than Ob- servers, or army corps Pilots, are killed or wounded. The infantryman is in greater peril than any of them.
The danger of flying is one thing, and the danger of aerial observation in actual warfare is another. The broad general principle is clear — if anything happens to the ship, there isn't much to do about it. In the recent war there was seldom a parachute, such as the balloonist has, to drop with. But the Balloon Observer has a serious and a dangerous mission, and although it is certainly less dangerous than that of the Airplane Observer, and certainly not so important in general, it is very important indeed in particular.
As to the danger and discomfort of balloon observation, it is acute, but it is very different from the danger and discomfort of airplane observation. For one thing, the stationary post of the balloon means that the fire from Archie is less. It is annoying, but only a few direct hits are made (Lieutenant Black says that no British balloon was ever brought down by enemy gunfire). Nevertheless, the heaving about of the basket by near-by explosions is rather more exciting than anything the flyer gets from the ground; especially since the balloon has to sit still and take its medicine, or quit entirely, and go down to earth. But to offset this, there is the hostile airplane which comes along, preferably early in the morning or late at night, and fires tracer bullets into the balloon, sending it down in flames. (The balloon doesn't explode; it burns.) The Observer has no possible means of defending himself, but on the other hand, he is often warned by telephone of the approach of a plane which he himself hasn't seen. That is why attacks are made at early morn and dewy eve — the attacking plane can't be seen so clearly either by the Observer or by the ground. The Observer can always demand to be hauled down; but in the end, if he is shot down, or sees that the destruction of the sausage is inevitable, his one recourse is to go over the side, and even then he has four great dangers. One is that the parachute won't open; one is that bits of the burning balloon fabric (for no method of fire-proofing it has ever proved successful) will graze and ignite the parachute; one is that the enemy airplane will follow him down, firing at him (although in view of the machine guns on the ground, this is dangerous to the enemy); and the last is that he may land in anything from a river to a mass of barbed wire. You would hardly believe that even a German would try to shoot an Observer coming down by parachute, but they did it — and more than one young man knows what it must feel like to be a partridge in the open season.