The light gathering should be almost 4 times more in the Newtonians, but: will there be a "break through experience" or just a bit more brightness and size? globulars, planetary nebulae and galaxies matter;-)
I had a 120 mm Orion Eon for two years. This is a 120mm F/7.5 FPL-53 doublet and probably better optically than your 120mm Binocular Telescope. I recently sold it because my generic 10 inch GSO Dob was the better all around performer and not just by a little. The Dob was better on the planets, it splits doubles not even worth looking at in the refractor. Globulars, nebulae, galaxies, for deep sky it's a break through experience.
As far as binocular Newtonian: In your situation, I would look very closely at a larger telescope with binoviewers. The advantage of a binocular telescope over binoviewers and a larger aperture telescope is that brighter exit pupils, lower magnifications are possible. Both are limited in brightness by the diameter of your dark adapted eye but the binoviewer will be 1/2 as bright.
But this advantage exists only at the larger exit pupils. At smaller exit pupils in the binocular telescope, the larger aperture with a binoviewer can make up for this loss of brightness with a larger exit pupil.
Consider a 10 inch binocular telescope and a 14 inch with a Binoviewer for someone whose dark adapted eye opens to 7mm. . If the 10 inch (250mm) binocular telescope is being used at a 5mm exit pupil, that would be 50x. the 14 inch (350mm) could be used with a 7mm exit pupil which would normally be twice as bright as the 5mm exit pupil (area) but since it is a binoviewer, it would be equal in brightness. This holds true for smaller exit pupils.
Exit pupils between 5mm and 7mm are useful but the vast majority of deep sky observing is done with smaller exit pupils. All planetary and double star viewing is done at smaller exit pupils. At smaller exit pupils, the binoviewer has several advantages. It is much simpler both mechanically and optically, it doesn't all the complexity of the collimating and aligning binocular telescope. In theory at least, it has the greater resolving power of the larger aperture. And it can be used alone as regular telescope. At the highest powers, looking for the smallest, most difficult objects, the "cyclops" mode with the larger telescope will go deeper.
I think the reason one reason larger binocular telescopes are so uncommon is that a binoviewer is an effective and less costly alternative.