In my earlier finite map benchmarks which compared several hash tables and functional maps (AVL trees and ternary trees), separate chaining (with $$\alpha = 0.47$$) beat double hashing ($$\alpha = 0.42$$) at unsuccessful searches (1% hit rate), but was slower at successful ones.
Theory predicts the following average number of probes for unsuccessful and successful lookups (expressions below): 
Separate chaining looks much better here, but the graphs are misleading, because we don't actually care as much about the load factor as about memory usage, so we want to compare the collision resolution schemes when the latter is the same.
If we use a linked list for the collision chain, this represents one word of overhead per item compared to double hashing. For instance, if the load factor with separate chaining is 1, we can afford to have a table twice as big with double hashing for the same amount of memory and a load factor of 50%. In other words, $$N + n = N'$$ where $$N$$ and $$N'$$ are the sizes of the tables for separate chaining and double hashing, and $$n$$ the number of elements. The respective load factors are
\[\begin{eqnarray*}
\alpha & = & \frac{n}{N}\\
\alpha' & = & \frac{n}{N'}\\
& = & \frac{n}{N+n}\\
\alpha' & = & \frac{\alpha}{1+\alpha}\end{eqnarray*}
\]The expressions for the average number of probes for unsuccessful and successful searches are (Knuth, TAOCP Vol 3, Section 6.4), for separate chaining
\[\begin{eqnarray*}
C_{u} & \approx & 1+\frac{e^{2\alpha}-1-2\alpha}{4}\\
C_{s} & \approx & 1+\frac{e^{2\alpha}-1-2\alpha}{8\alpha}+\frac{\alpha}{4}\end{eqnarray*}
\]and for double hashing,
\[
\begin{eqnarray*}
C'_{u} & \approx & \frac{1}{1-\alpha'}\\
C'_{s} & \approx & -\frac{\ln(1-\alpha')}{\alpha'}\end{eqnarray*}
\]These are the expressions plotted above, for $$\alpha = \alpha'$$, which, as I said, is not what we want, as $$\alpha' = \frac{\alpha}{1+\alpha}$$ if the memory use is to be the same. By substituting this in the expressions for $$C'_u$$ and $$C'_s$$, we get these graphs, where the abcises represent the load factor in the table with separate chaining. 
Separate chaining tolerates load factors over 1, which correspond to $$\alpha' < 1$$, so we can complete the plots: 
Comments
I've quite liked José Nuno Oliveira's insight about hash tables with separate chaining being the quotient of the set of keys by the equivalence relation induced by the hash function. This means that, in general, the separate chains can be stored in an arbitrary lookup datastructure. Even though one tends to "forget" the overhead incurred in maintaining the chains, it opens the door for bootstrapping hashtables à la Okasaki. What happens if α ≫ 1 but the chains are stored in an efficient lookup structure? What if the chains are themselves efficient hashtables? I guess this means that there is a continuum between hashing with linear chaining and n-uple hashing, and that α = 1/2 is somehow a magic number.