Consider the following test-case.

test.h:
...
struct aaa
{
  template<typename T> void foo(T obj) {}
};
...

test.cc:
...
extern void other_unit (void);

#include "test.h"

struct aaa var;

int
main (void)
{
  int a;
  float f;
  var.foo (a);
  var.foo (f);
  other_unit ();
  return 0;
}
...

test2.cc:
...
#include "test.h"

struct aaa var2;

void
other_unit (void)
{
  double d;
  var2.foo (d);
}
...

Compiled like this:
...
$ g++ test.cc test2.cc -g
...

In the test.cc compilation unit, we have:
...
 <1><f0>: Abbrev Number: 2 (DW_TAG_structure_type)
    <f1>   DW_AT_name        : aaa
    <f5>   DW_AT_byte_size   : 1
    <f6>   DW_AT_decl_file   : 2
    <f7>   DW_AT_decl_line   : 1
    <f8>   DW_AT_sibling     : <0x143>
 <2><fc>: Abbrev Number: 3 (DW_TAG_subprogram)
    <fd>   DW_AT_external    : 1
    <fd>   DW_AT_name        : (indirect string, offset: 0x1d0): foo<float>
    <101>   DW_AT_decl_file   : 2
    <102>   DW_AT_decl_line   : 3
    <103>   DW_AT_linkage_name: (indirect string, offset: 0x262): _ZN3aaa3fooIfEEvT_
    <107>   DW_AT_declaration : 1
    <107>   DW_AT_object_pointer: <0x116>
    <10b>   DW_AT_sibling     : <0x121>
 <3><10f>: Abbrev Number: 4 (DW_TAG_template_type_param)
    <110>   DW_AT_name        : T
    <112>   DW_AT_type        : <0x158>
 <3><116>: Abbrev Number: 5 (DW_TAG_formal_parameter)
    <117>   DW_AT_type        : <0x15f>
    <11b>   DW_AT_artificial  : 1
 <3><11b>: Abbrev Number: 6 (DW_TAG_formal_parameter)
    <11c>   DW_AT_type        : <0x158>
 <3><120>: Abbrev Number: 0
 <2><121>: Abbrev Number: 7 (DW_TAG_subprogram)
    <122>   DW_AT_external    : 1
    <122>   DW_AT_name        : (indirect string, offset: 0x254): foo<int>
    <126>   DW_AT_decl_file   : 2
    <127>   DW_AT_decl_line   : 3
    <128>   DW_AT_linkage_name: (indirect string, offset: 0x1db): _ZN3aaa3fooIiEEvT_
    <12c>   DW_AT_declaration : 1
    <12c>   DW_AT_object_pointer: <0x137>
 <3><130>: Abbrev Number: 4 (DW_TAG_template_type_param)
    <131>   DW_AT_name        : T
    <133>   DW_AT_type        : <0x1af>
 <3><137>: Abbrev Number: 5 (DW_TAG_formal_parameter)
    <138>   DW_AT_type        : <0x15f>
    <13c>   DW_AT_artificial  : 1
 <3><13c>: Abbrev Number: 6 (DW_TAG_formal_parameter)
    <13d>   DW_AT_type        : <0x1af>
...

And in the test2.cc compilation unit, we have:
...
 <1><25b>: Abbrev Number: 2 (DW_TAG_structure_type)
    <25c>   DW_AT_name        : aaa
    <260>   DW_AT_byte_size   : 1
    <261>   DW_AT_decl_file   : 2
    <262>   DW_AT_decl_line   : 1
    <263>   DW_AT_sibling     : <0x289>
 <2><267>: Abbrev Number: 3 (DW_TAG_subprogram)
    <268>   DW_AT_external    : 1
    <268>   DW_AT_name        : (indirect string, offset: 0x2b7): foo<double>
    <26c>   DW_AT_decl_file   : 2
    <26d>   DW_AT_decl_line   : 3
    <26e>   DW_AT_linkage_name: (indirect string, offset: 0x27b): _ZN3aaa3fooIdEEvT_
    <272>   DW_AT_declaration : 1
    <272>   DW_AT_object_pointer: <0x27d>
 <3><276>: Abbrev Number: 4 (DW_TAG_template_type_param)
    <277>   DW_AT_name        : T
    <279>   DW_AT_type        : <0x29e>
 <3><27d>: Abbrev Number: 5 (DW_TAG_formal_parameter)
    <27e>   DW_AT_type        : <0x2a5>
    <282>   DW_AT_artificial  : 1
 <3><282>: Abbrev Number: 6 (DW_TAG_formal_parameter)
    <283>   DW_AT_type        : <0x29e>
...

Despite the fact that the two DIEs are generated from the same header file, they are structurally different, due to the different instantiations of the member function template. Consequently, dwz does not factor out the DIEs.