How much do you weigh & what size sail are you using and in what wind condtions? Do you have single or double straps on the back of both boards?
Roger will be along to offer some help, but in the mean time, here are my thoughts. It's my experience that there is little difference between my 105 L board and my 85 L board when it comes to getting into the straps.
The critical issue is speed. With the smaller board, you have to be moving faster when reaching for the strap with the back foot. If not, you will place too much weight on the tail of the board, which will cause it to sink, stall and head up into the wind.
You may also want to measur the distance between the front and back straps on both boards to see if there is a difference. IF you have to reach a longer distance on your smaller board, that may be part of the problem.
For me it's difficult to get into the back strap on a beam reach because I can't get much weight off my back foot, but if I head up a bit, then I can get more weight on the front foot and harness to free up my back foot. Careful not to head up too or you stall, maybe 30 degrees.
I also place my back foot on the board in front of the strap before heading up, so that I don't have to move it far to get into the strap. With lots of repetition, the step into the strap becomes automatic.
Hope this helps.