Advantage is you can get higher gravity with limited systems as well if I recall correctly the mash has a saturation point with the sugars somewhere in the 1.080's (someone correct me if I'm wrong as I would be interested to know) so that is your maximum first running gravity.
The more grain you use the more you have to sparge to get your efficiency, so it is diminishing returns the higher the gravity because you end up with so much wort that it would take longer and longer to boil down.
The disadvantage of DME/LME is what I said previously, it tends to not attenuate as well AG as you cannot play with the mash schedule to get a highly fermentable wort, its fermentability is pretty much set by whatever company makes it depending on their mash schedule.
As a side note, IMO, I generally do not make high gravity beers so my experience is limited. However, the only 1.1+ gravity beer I made (when I just started out brewing...of course new brewer going for a big beer syndrome) was cloyingly sweet. What I learned is you need to dry those big beers out to make them drinkable, that means adding sugar to get a balance. I assure you if you get 10-20% of your fermentables from sugar in a 1.109 beer you will still have plenty of body.