= Solution
At a common large threshold b, the header tail has exponent $-\log\rho$, whereas the payload tail has exponent $1-\rho$. Since $-\log\rho>1-\rho$ for $0<\rho<1$, \b[the payload <queue> has the heavier tail and dominates overflow on the large-buffer exponential scale at fixed load]. The inequality follows from the <strict convexity> of minus the <logarithm>, or from integrating $1/u>1$ between rho and one.
The explanation is that a header always consumes one slot, while a payload can be unusually large. A rare accumulation of work can therefore overflow the byte buffer without accumulating as many as 1000 packets. Replacing every payload by its <mean> would lose precisely this source of variability.
For the actual capacity 1000, retaining the exact continuous-time prefactors gives a qualification that a tail-exponent comparison alone cannot detect. The two infinite-buffer proxies are $p_H=\rho^{1000}$ and $p_P=\rho e^{-1000(1-\rho)}$, and
$$
\boxed{\log\frac{p_P}{p_H}=999(-\log\rho)-1000(1-\rho).}
$$
Thus payload overflow is more likely under this proxy exactly when the displayed expression is positive. For ordinary loads it is positive; for example it is positive at $\rho=0.9$. At $\rho=0.999$ it is approximately $-0.00050017$, so the header proxy is slightly larger. Consequently, without a numerical load, there is no universal exact ordering for the fixed capacity, although the large-buffer exponential ordering is unambiguous. Very near full utilization both 1000-unit buffers have substantial tail probabilities, so equal numerical capacities alone do not establish that the design is sensible. These are the requested infinite-space estimates, rather than an exact loss model for the interacting finite buffers.
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