Let me see if I can explain my thoughts on this.
Breastfeeding and bottlefeeding each require energy expenditure. Each
has its own set of skills and challenges
especially for premies.  Bear in mind I have bottlefed many premies in
my career as a nicu nurse, and I've
assisted many premies to breastfeed in my career as a nicu nurse and
then LC. I still feed premies when I help
in the nsy on busy days, and I still assist premies to bf. Term babies too!
So, the bottle is *easier* to get started and, depending on the nipple
used and the way the bottle is held and the
baby is paced, the flow can be much faster than the breast. But the
bottle can be difficult for the infant to control
and coordinate and the infant can certainly fatigue and give up.
The breast, especially in the colostrum phase or when mothers are
trying to breastfeed in a hospital environment
and possibly under timed or other controlled-by-other conditions, can
be *harder* to get started (let down) and
the baby may not get much volume in the allotted time, or may actually
stop sucking in response to slow flow.
This could be interpreted as tiring out. And I am sure over time
babies do tire out. The mother may also have a low
supply due to being separated, conditions of the preterm birth etc.
So I am not convinced that breastfeeding requires more *energy* than
bottlefeeding.
As an aside, it makes me crazy when babies are felt to need a higher
calorie formula, like 22 cals. I see this alot.
A baby that is not gaining weight due to taking in not enough volume,
is given a special expensive formula, and has
to get that one from WIC, when he is taking 1 oz every 3 hrs, that is
giving him 16 extra cals per day. Is that really
making any difference in weight gain? No, it doesn't, but it makes
mother think it's such a special formula.
The baby wil gain as he is able to take more volume.  Ugh!
Laurie Wheeler RN MN IBCLC
Mississippi USA

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