Why does radical chlorination and bromination of propane occur at different positions?
The Hammond Postulate (HP): Exothermic reactions have early transition states (TS). Endothermic reactions have late TS's. [The HP may easily be demonstrated with a retractable, metal tape measure. Open several feet of the tape with the left hand holding the case and the other hand at the end of the tape. Bend the tape upward so that it looks like a TS. Raise your left hand above the right. This is an exothermic reaction. Note how the high point (TS) moves to the left. Make an endothermic reaction. Watch the TS move to the right.]
To compare the radical chlorination and bromination of propane, the following chart is instructive. Only the first propagation steps need to be examined because this is where the 1o vs. 2o choice is made. Chlorination (A &amp; B) is exothermic (earlier TS) for both C-H bonds with the secondary more favorable by virtue of the weaker 2o C-H bond. Bromination (C &amp; D) is endothermic (later TS) and more reversible than chlorination. The difference in the heat of reaction in both chlorination and bromination is 2 kcal/mol with the secondary radical formed in favor of the primary radical. But this equal difference does not explain the difference in the greater selectivity in the bromination vs. chlorination. The difference in activation energy (Ea) in the TS between secondary C-H bond cleavage vs. primary is greater in the bromination than in chlorination. [ADDENDUM: The &Delta;&Delta;H&#8225; (&Delta;Ea) for chlorination is 1 kcal/mol; for bromination, 3 kcal/mol. Therefore, bromination is more selective.][2] [continued] 





The data for methane in the chart below is instructive. Fluorination has a very low Ea and it is more exothermic than chlorination. A fluorine atom is virtually indiscriminate in choosing among primary, secondary and tertiary C-H bonds. The less reactive chlorine atom has a higher Ea and shows greater discrimination. While these two halogenations are readily conducted at ambient temperature, bromination is conducted at elevated temperature to obtain useful rates of reaction. With a high Ea selectivity is the greatest with bromination. 
To put a folksy spin on the discussion, a bromine atom has more "time" to make choices as to what C-H bonds it is capable of breaking while a fluorine atom is virtually a bull in a china shop.




[2]: Streitwieser and Heathcock, Introduction to Organic Chemistry, 4th ed., pg. 114.