I have been playing with the Asics 116 for two months now and can tell you a lot about it and to a much lesser extent the 125. I have never tried the 109 and in fact never seen anyone around here using it.
For some background, I am an older 4.0 player that plays about 2 1/2 hours a day. Prior to switching to the Asics 116, I was using the newest version of the Prince EX03 Red.
First the 125 - I tried it once and it, like most oversized rackets, appears to be designed for someone that doesn't swing very hard and wants additional power. Around here, at least, that is mostly women and older players. I have never liked oversize rackets so it didn't appeal to me. I felt that I had less control and found it slower to quickly position the racket for a volley or a shot that I had to scramble to get. Still, the players that traditionally use oversize rackets seem to like it a lot. Note: you CANNOT string the 125 with a 40 foot string.
By the way, these are brand new rackets designed from the ground up, not a repaint on an old Head racket as suggested earlier.
Now on to the 116. First, in spite of the 116 measurement it is actually not an oversized racket in the traditional sense. It is effectively a mid-plus racket, like the Prince EX03 Read 105 I was using before. If you put the 116 on top of the Prince 105, the head size is almost the same. The additional overall size is just that the the head is elongated.
The 116 has noticeably more power than the 105 but no less control. It has a very low swing weight which is very close to the Prince 105, which made for a very easy transition. Because of its very low overall weight I can quickly position it for a fast volley return or scrambling after a wide serve or shot. My serve is definitely faster as well. In spite of the stiffness of the frame I have not had any elbow problems with the racket, even though I am prone to this with some rackets I have used in the past (not the Prince rackets which seem to be very easy on the elbow).
By the way, this is a very easy racket to string (I string my own rackets), especially compared to the Prince rackets with the large side holes!
My wife, who is a 4.0 to 4.5 level player is also switching to the 116 as soon as they are in stock. I think the chart referenced earlier in this thread is essentially correct about the NTRP level for the 116: 3.0 to 4.5.