It is utter rubbish if anyone claims economy to be better in a traditional torque-converter driven automatic, these are inefficient by design.
In theory a DSG should at worst be no worse than a manual when driven normally in D, and are potentially better - it really depends on how good the software is. Yes they are slightly heavier than a manual by about 25kg or so but this is negligible and would lose only a fraction of a percent in overall economy - under-inflated tyres would be far more noticeable.
In my experience the D mode in my Stronic TTS was pretty good and and would change up through the box very quickly, you would be in 6th by 35mph.
Conversely the Stronic in the RS, again in my experience, is nowhere near as good and frustrates the hell out of me, a manual would easily be more economical around town, but the Stronic has a longer top gear which helps a lot on a run.
Around town you have to be on the ball and often change up manually to get the best economy possible as the software insists on holding onto gears until 2krpm. If I was driving a proper manual then if performance is not needed I would change up around 15krpm which would drop the revs down to 1100 - absolutely fine with this engine.
This means in the RS you can be in slow traffic and be me moving with engine speed at screaming at 19.5krpm in 2nd gear with virtually no throttle load so you
should be in 3rd - however the only way to get into 3rd is to accelerate past 2krpm or change manually. In the S under same throttle load conditions it would've changed into 3rd a lot lot sooner = better economy.
If I could request one change to the software it would be to lower the shift point in D by 2.5krpm for light throttle loads (although not changing down to 1st gear automanually would run a very close second

). This would yield much better economy.