I'm assuming that you are talking BJT current mirrors here.
Particulatly at low Ic, the beta rolls off a lot (variable w/
processing, worse at low temp, etc.). The Ib demand from
every transistor in the mirror-rack subtracts from the pilot
current to the mirror, causing an inaccuracy. Your 1:1
ideal ratio might become 1-(N/hFE):1 (N base currents,
being Ic/hFE apiece, skimmed off the top and the mirror
devices each output only a copy of the residual). If you
have a plurality of outputs, it only gets worse.
For example, suppose you have an NPN mirror rack with
one input, 4 outputs, Ic=10uA, hFE @ 10uA = 50 worst case.
Ib=10uA/50=200nA. Total base load is 1uA. So pilot collector
current is 9uA and you will expect the same 9uA out the
slave collectors. That's a 10% error. And if you are trying to
dead-balance a NPN mirror output against a PNP mirror output,
is the PNP (even if similar beta) then going to push 8.1uA
vs the 9uA, another 10% of raw imbalance and a certain Vio
contributor?
Now with the beta helper, that 1uA of lost pilot Ic (N*Ib)
is buffered down to maybe 20nA (assuming beta is the same,
2 decades down; surely not, but close enough to illustrate).
So you would be getting something like 10uA:9.9uA, a much
better mirror fidelity.
What to worry about in the buffered current mirrors is base
impedance, charge pumping, noise amplification - the low
emitter impedance is good in a small signal sense, looks
great, but large signal you can get into relaxation oscillation
(because the emitter pushes hard one way, but cannot
pull at all). You may need to add some extra passive load
to the base rail which is not ideal for low power, but may
make the circuit more robust when perturbed away from
normal operating point.