How to decide at which end to start the numbering of the parent chain when the options for locant sets are the same?
If numbering from each end of the parent chain gives the same set of locants, the next criterion stipulates that lowest locants are assigned to the substituent that is cited first as a prefix in the name.

On this matter, the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:


  P-14.4 NUMBERING
  
  When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
  
  (…)
  
  (f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
  
  (g) lowest locants for the substituent cited first as a prefix in the name;
  
  (…)


Note that Rule f takes precedence over Rule g. If no decision can be attained by application of P-14.4(f), the lowest set of locants is selected according to P-14.4(g) in their order of their citation in the name.

This means in effect that alphanumerical order is used to establish the numbering when a choice is possible since alphanumerical order is used to establish the order of citation of substituent prefixes in the name.


  P-14.5 ALPHANUMERICAL ORDER
  
  Alphanumerical order has been commonly called ‘alphabetical order’. As these ordering principles do involve ordering both letters and numbers, in a strict sense, it is best called ‘alphanumerical order’ in order to convey the message that both letters and numbers are involved
  
  Alphanumerical order is used to establish the order of citation of detachable substituent prefixes (not the detachable saturation prefixes, hydro and dehydro), and the numbering of a chain, ring, or ring system when a choice is possible.
  
  (…)
  
  P-14.5.1 Simple prefixes (i.e., those describing atoms and unsubstituted substituents) are arranged alphabetically; multiplicative prefixes, if necessary, are then inserted and do not alter the alphabetical order already established.


For example ‘dibromo’ comes before ‘chloro’ since ‘bromo’ begins with ‘b’, ‘chloro’ begins with ‘c’, and the multiplicative prefix ‘di’ does not change the alphabetical order.

However, the example given in the question does not include simple prefixes but the compound substituents ‘1,1-dichloroethyl’ and ‘2-bromo-1-chloroethyl’. Such compound names are considered to begin with the first letter of their complete name.


  P-14.5.2 The name of a prefix for a substituent is considered to begin with the first letter of its complete name.


Therefore, the correct name for the compound given in the question is 4-(2-bromo-1-chloroethyl)-5-(1,1-dichloroethyl)octane since ‘2-bromo-1-chloroethyl’ starts with ‘b’ and ‘1,1-dichloroethyl’ starts with ‘d’.