I wanted to know once that as mvas above said "an increase of 1 magnitude, from 13 to 14.5" if the limiting magnitude increases only by 1 then what other significant changes do DSOs show?
Well, there's a bit more to seeing and seeing details in DSO objects than just the "ideal conditions" aperture/magnitude gains cited by mvas above. Those numbers cited refer to the limiting stellar magnitude for each aperture, figuring out the visibility (limiting magnitude) of non-stellar DSO objects is a bit more convoluted...
The number one factor will be the amount of light pollution that you will be contending with at your observing location. Case in point, here's a link to a light pollution map for my club's public observing site in NY...
ClearDarkSky Light Pollution Map: Ward Pound Ridge Reservation, Cross River, NY
http://www.cleardark...=great red spot
...the cross hairs indicate that we observe from a, um, "moderately" light polluted and relatively, er, "not-so-good" location in an "Orange Zone". Comparing the performance of your current 130EQ vs your desired 10-inch GSO Dob at that site the larger scope will, of course, reveal more DSO's and more detail in those objects than the smaller scope but neither scope will be performing to their potentials based on the light pollution washing out vital contrast details. The limiting-magnitude for DSOs will improve in darker green, blue, and black locations and lessen the closer one observes to red, grey and white zones.
You can discover the light pollution from your location either here...
Clear Sky Chart Homepage:
...where you can learn about other contributory what other factors like atmospheric transparency, seeing, darkness, wind, humidity and temperature will be like at your location, as well. Or you can discover your light pollution zone here...
Light Pollution Atlas 2006:
...so there are a lot of factors that will go into what one can and cannot see in DSO with their particular telescope on any given night. But, for sure, optical quality between the two being equal, the larger scope will "go deeper" for DSOs and provide greater resolution for the planets...conditions permitting!