Will a 30mm scope give me more than a 1" dia. scope on a  ar-15 rifle?
Leupold brand good to go with either size?

A good 1" optic can deliver light transmission and clarity as well as a 30mm, however some 30mm scopes allow for more internal windage and elevation adjustment.  The exit pupil in either size lens will deliver enough light to your eye.   Advanced coatings will also enhance light transmission and improve clarity.

Due to larger lenses and larger diameter tubes, 30mm scopes tend to be heavier.

You should be good to go either way if you're investing in a Leupold optic.

Give you more what?  If you are comparing the VX-R Patrol and Mark AR, there are quite a few differences, and it is not just tube diameter.

Yes, Leupold is reliable, both models, but making a choice between the two versions depends on what your use, needs, and expectations are.

I chose the 30mm main tube VX-R Patrol and consider it worth the extra cost.  The glass quality is significantly better, although the Mark AR is not bad.  Light transmission in the Patrol is much better, but not because of tube diameter.  The size of the beam of light after it passes through the front end objective lens assembly is very small and 30mm vs. 1 inch makes no difference in light transmission.  The notion that somehow 30mm tubes produce "brighter" scopes than 1" tubes is entirely false.  However, the legend gets passed on because most 30mm main tube scopes just happen to also have much better quality lenses and optical quality, irrespective of tube size.  The "brightest" scope I own is a 1" main tube Kahles.  It has better optical quality because of the better glass, coatings, and other optical components, not the main tube size.  

Where 30mm tubes can help is in elevation and windage adjustment range, since there is more internal room for the erector assembly to move up and down and back and forth.  However, Leupold on the VX-R chose to use a 1" 3x erector assembly, so there is no real difference in elevation or windage range.  It does not really matter, however, unless you plan to shoot beyond about 700-750 yards, because the internal adjustments are sufficient to get you out that far in either scope.

The Firedot reticle in the Mark AR is green.  In the Patrol it is red.  Both use the same motion activation illumination system, otherwise, except the Patrol version has more illumination brightness settings or positions, eight, I believe compared to 6 on the Mark AR.  Both use the same milrad turrets and both are accurate and repeatable.  The 30mm tube is much stronger, being made of thicker aluminum, and is accordingly a couple ounces heavier.  The Mark AR is lighter.

The real difference is the quality of the glass.  Mark AR is good.  Patrol is very, very good.  It is not just lens quality.  There is better attention to internal light reflection mitigation, lens coatings and edge blackening of the lenses.  This is not so noticeable during good light.  It is quite noticeable in low light at dawn and dusk.

Either will hold up to heavy use.  Under extreme conditions, the 30mm tube will take more abuse.  

I want a vxr -patrol ,,,but for right now ,,,I already have a vxiii-3.5x10x40 I can use and try out now on my new 300 Blackout until I can save up some vxr-coupons?
I just worry about the recoil breaking the Leupold.

Recoil breaking the Leupold?  My Weatherby Mark V in 300 Weatherby Magnum and several Remington and Winchester 7mm Magnum bolt guns either now or in the past or have worn Leupold scopes with no problems.  Other long action bolt guns,  with '06 type power, too with much higher recoil than your rifle.

300 Blackout is down on the power scale with a .30-30.  Even baseline entry level scopes from most Asian manufacturers above the junk level can handle that.  Optical quality is another issue.

The scope will not have recoil problems.  None of my other scopes from many different major manufacturers have either.  Relax about the recoil of  the little 300 Blackout, or even .308 or higher with any modern scope from a name manufacturer, and focus on optical quality and features you desire.  I use a Burris on my .45-70 and consider the Leupold scopes at least as stout.  I've never had a Leupold reticle detach or one of their scopes fail to hold zero or have any kind of mechanical failure in over 40 years.