The larger the front lens is, the more light the scope can let in. The usable light that reaches your eye is dependant on the front lens diameter and the magnification (power) of the scope as well as lens coatings and the ability of the optics to transmit light thru the scope. Take a look at the rear lens of your scopes as you hold them away from you: you will notice that the diameter of the Daisy scope image (exit pupil diameter) will be a little less than 4mm, the Simmons' exit pupil will vary from just over 4mm at 3x to just over 13mm at 3x. Depending on your age, your eye's night-adapted pupil will range from 5mm to 7mm. Simply put, the Simmons lets more light thru to your eye. If you try using it at 9x, you probably won't notice much difference as compared to the Daisy. Neither of the scopes you have is high quality, but they do what you want, but take a look at a Nikon or another of the better scopes to see what a difference good quality makes!
As far as the Simmons being hard to use on bright days, it probably has a fine crosshair and the Daisy's is probably coarse.
Take a look at the Crosman airgun scopes, they seem to be pretty good. I have been using one on my .17 HRM rifle until I bought a BSA Sweet 17 scope. My 4 x 10X Crosman will soon be listed in the classifieds.