In both Atlantic City and Las Vegas, the game program chip in multi-denomination slot machines includes separate programs for each different denomination. Each game has its own theoretical payback percentage.
If playing multi-denomination machines online, we've been told that their is only one program with one setting having all the different denominations operating with the same payback percentage at the same time.
If that was in fact true; are there any added advantages for the casino or the player while the game is operating under these two different formats?

Frankly, I don't know if either of the two assertions you make are in fact true. They probably are, but I don't really know.
I think all this 'denomination' stuff about slot machines is deceptive. I hear about a Penny Slot and I sure don't see very many people putting in a lone penny and then pulling the handle on it. It sure is strange sit at a Dollar machine and put in five of them per spin. So if by Multi Denominational they mean I can stay seated there and select rather than amble around the place and select, I sure don't consider there to be all that much difference.
The Gaming Board apparently reports MultiDenominational machinces differently than the Sole Denominational machines. I don't see much of a difference in the adjectives though.

A multi-denomination machine just means the player could select pennies, nickles, quarters or dollars before playing at the same game. Nevada G.C. requires each separate denomination to have its own program within the game therefore every denomination would have its own theoretical payback percentage, as chosen by the casino. This regulation requirement is for stand alone machines as well as server based. I'm certain if the casino chose they could also have all denominations set the same. But according to 'Casino Player' magazine most casinos lower their hold for each larger denomination the player selects.
It is impossible to read any gaming regulations regarding Online Casinos and for some reason the alleged regulators keep this information along with any other requests for regulations a guarded secret. I personally e-mailed along with sending via snail mail written requests to five different online gaming regulator jurisdictions requesting gaming regulations, and didn't even get a response from one of them that they even received my requests. Online casino reps. that communicate to players via forums also refuse to engage in any discussions regarding regulations. Online gamers should assume if their are any gaming regulations that even exist, they certainly aren't being enforced.
Most online slot games are multi-denomination games. An alleged online gaming technician (programmer) once posted that all online multi-denomination games, have only one setting or program within meaning that all would operate off whatever this one setting the operator selected.
My question is having the option to play under each of these two different programming formats, does one or the other offer a better advantage for the player?

As to online regulations, the promulgator of such regulations probably doesn't really exist as anything but a rubber stamp in some lawyers office.
As to selecting one of several RNGs versus using the only RNG in there, I don't see much of a difference. I'll wait for others to post and perhaps get a new perspective on just what is up here.