Are gravastars observationally distinguishable from black holes? Are observations of Hawking radiation at the acoustic event horizon in Bose-Einstein condensates consistent with gravastars?
To reconcile the second law of thermodynamics with the existence of a black hole event horizon, black holes are necessarily said to contain high entropy while gravastars not at all. An event horizon forming out of a collapsing star's intense gravity sufficient enough to force the matter to phase change transforming into Bose-Einstein condensate would be such that nearby matter would be re-emitted as another form of energy, and all matter coming into contact with the event horizon itself would become incorporated.
So, it seems reasonable to wonder if black holes are distinguishable from gravastars since gravastars appear to be better emitters, and black holes better entropy sinks. What do observations of Hawking radiation from acoustic black holes from Bose-Einstein condensate seem to suggest?
 A: Fact: quantization of gravity is still at a research stage, only effective quantized field theories are used.
Fact:gravastars ( had to look it up) belong to one proposal for quantizing gravity, which is not particularly dominant in the research .

A gravastar is an object hypothesized in astrophysics as an alternative to the black hole theory by Pawel O. Mazur and Emil Mottola. It results from assuming real, physical limitations on the formation of black holes. These limits, such as discrete length and time quanta (chronon), were not known to exist when black holes were originally theorized, so the concept of a gravastar is an attempt to "modernize" the theory by incorporating quantum mechanics. The term "gravastar" is a portmanteau of the words "Gravitational Vacuum Star".

Chronons belong to this specific hypothesis for replacing black holes by a quantum mechanical equivalent, and this is the first time I met them, though a particle physicist.
The question

So, it seems reasonable to wonder if black holes are distinguishable from gravastars since gravastars appear to be better emitters, and black holes better entropy sinks. 

is comparing apples with oranges. Black holes come from classical General Relativity. Gravastars  belong to a model of quantized general relativity.
(The application of quantum field theory at the horizon of a black hole giving Hawking raditaion, does not turn the black hole from a classical singularity to a quantized gravitational one.) 
String theories allow for quantized gravity and at the same time can embed the standard model of particle physics.
There is a string theory based model which turns black holes to fuzzballs.

Fuzzball theory replaces the singularity at the heart of a black hole by positing that the entire region within the black hole’s event horizon is actually a ball of strings, which are advanced as the ultimate building blocks of matter and energy. 

Since physicists expect that a definitive model of quantization of gravity is waiting in the future, it is fuzzballs ( and other similar proposals in quantization of gravity) that have to be compared with gravastars, not classical black holes. And then  experimental evidence has to be sought.
A: If we insist on restricting to acoustic analogues,
The "Hawking" effect in acoustic systems comes from the behaviour of wave mechanics around what is very loosely an event horizon; a region where characteristics of the fluid all point in the same direction. The system turns out to emit sound waves with a thermal spectrum. This analogy relies on the black hole being actually a black hole.
If real black holes are in fact ``gravastars", or whatever, then they would have different physics from those that acoustic black hole simulations try to model. The fluid mechanical analogues would still be analogues to general relativity black holes, and not to the actual astrophysical objects. So you couldn't determine their properties by studying dumb hole systems.
Perhaps you are thinking that whatever mechanism forces black holes to be "Gravastars", etc, would also hold in the fluid-mechanical case. But there is no reason to expect this; the wave mechanics that give Hawking-like behaviour around dumb holes are perfectly mundane and established, there is no black hole information paradox to be avoided in this case, and nothing analogous to the supposed quantization of spacetime that such ideas usually rely on.
A: Hawking radiation (which hasn't been observed experimentally at all, let alone with sufficient resolution to use it diagnostically) isn't really the way to go here. Your best bet is gravitational wave ringdown after binary black hole mergers.
I link to a PRL Synopsis that summarizes a line of papers that ask more or less your question: https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.116.171101 , in terms of the aforementioned ringdown effect.
After a black hole merger, the now-isolated event-horizon is in a non-equilibrium state. Roughly because of the no-hair theorem the merged black hole has to radiate away its asymmetries, converging towards a Kerr solution. The wobbles in the apparent horizon resulting from this resemble a ring rotating about a pole, so the process is called "ringdown". The details of this process can be calculated with very good precision from analytic perturbation theory.
The above line of papers argues that the signal emitted from this process is in fact different from a black hole vs other similar objects. The example they use is a wormhole, but this is more of a proof of principle than a serious suggestion that wormholes exist. A wormhole has two light-rings rather than one, which leads to a resonant-cavity effect as the ringdown signal scatters off of each. This results in visible modulation in the ringdown signal that are not present for black holes.
Subsequent papers show similar effects for non-black-hole compact objects. A gravitational wave that falls into an event horizon will never come out, and there will be no extra modulation. But a merely-very-deep gravity well has two edges, which leads to a similar (but weaker) cavity effect as in the wormhole. The wave scatters off both edges of the gravity well, as it first falls in and then climbs back out.
It's worth pointing out, however, that as a strict matter of principle one can never truly prove an object to be a black hole. Suppose, for example, that I am standing on the centre of a collapsing star. I wait until a few Planck second before the event horizon forms, and then detonate a bomb that arrests the collapse. There is no black hole, and eventually observers on Earth will see the star blow back up. But because of gravitational time-dilation that could take many billions of years of Earth time, during which the collapsing star would appear identical to a black hole.
