What method should I use to identify which variables differentiate between objects of two different classes? To illustrate the problem posed by the question: Consider the problem of differentiating  between consumers who belong to two different segments. I could use a naive or a sophisticated approach as outlined below. 
The question is: what is the benefit to using the sophisticated approach?
Naive Approach
Compute the summary statistics (e.g., means, frequencies) of all the available variables (e.g., income, age etc) and then see how the groups differ on these variables by inspecting the table of summary statistics.
Sophisticated Approach
Use logistic regression to identify which variables (e.g. income, age, etc) predict class membership.
Why use the sophisticated approach over the naive one?
 A: Take a simple case: two categorical predictors, $x_1$ & $x_2$, of segment, $y$.
For $x_1=0$ :
$\begin{array}{ccc}
 & y=0 & y=1 \\
x_2=0 & 1 & 2 \\
x_2=1 & 4 & 2 \end{array}$
For $x_1=1$ :
$\begin{array}{ccc}
 & y=0 & y=1 \\
x_2=0 & 2 & 4 \\
x_2=1 & 2 & 1 \end{array}$
The first approach you describe ignores all the data in the body of the three-way contingency table & looks only at the marginal tables:
$\begin{array}{ccc}
 & y=0 & y=1 \\
x_1=0 & 5 & 4 \\
x_1=1 & 4 & 5 \end{array}$
&
$\begin{array}{ccc}
 & y=0 & y=1 \\
x_2=0 & 3 & 6 \\
x_2=1 & 6 & 3 \end{array}$
I don't know what predictions you would make from these, say for an individual with $x_1=1$, $x_2=1$ - because you haven't said - but it's clear that any information about association or interaction between the predictors has been lost. For continuous variables you would, I gather, discard still more information by reducing the whole marginal distribution to its mean.
Logistic regression will of course fit $\log\frac{\Pr(Y=1)}{1-\Pr(Y=1)}=\log 2 + x_2\log\frac{1}{4}$, using all information in the body of the table to either estimate parameters or assess model fit; any predictive modelling approach worth its salt will do something similar.
Not that it isn't worthwhile to describe the characteristics of each segment, either as an end in itself or as a prelude to a predictive model.
