Only one line is different (the second one), and one can deal with several kind of parameters, while the other can't :

----------------------- Works :
let string_d =
    let t = 3.1 in
    (fun brick_name brick_verb verb x ->
    Printf.ksprintf (fun s ->
             if verb <= brick_verb
             then Printf.printf "[%s]%s" brick_name s else ()) x)
;;


----------------------- Doesn't works :
let string_d =
    let t = Sys.time () in
    (fun brick_name brick_verb verb x ->
    Printf.ksprintf (fun s ->
             if verb <= brick_verb
             then Printf.printf "[%s]%s" brick_name s else ()) x)
;;



----------------------- PROF :



let string_d =
    let t = 3.1 in
    (fun brick_name brick_verb verb x ->
    Printf.ksprintf (fun s ->
             if verb <= brick_verb
             then Printf.printf "[%s]%s" brick_name s else ()) x)
;;
            Characters 23-24:
      let t = 3.1 in
          ^
Warning 26: unused variable t.
val string_d : string -> 'a -> 'a -> ('b, unit, string, unit) format4 -> 'b =
  <fun>
# string_d "brickname" 5 1 "bonjour %s" "hi";;
[brickname]bonjour hi- : unit = ()
# string_d "brickname" 5 1 "bonjour %d" 4;;
[brickname]bonjour 4- : unit = ()
# let string_d =
    let t = Sys.time () in
    (fun brick_name brick_verb verb x ->
    Printf.ksprintf (fun s ->
             if verb <= brick_verb
             then Printf.printf "[%s]%s" brick_name s else ()) x)
;;
            Characters 23-24:
      let t = Sys.time () in
          ^
Warning 26: unused variable t.
val string_d :
  string -> '_a -> '_a -> ('_b, unit, string, unit) format4 -> '_b = <fun>
# string_d "brickname" 5 1 "bonjour %s" "hi";;
[brickname]bonjour hi- : unit = ()
# string_d "brickname" 5 1 "bonjour %d" 4;;
Characters 25-37:
  string_d "brickname" 5 1 "bonjour %d" 4;;
                           ^^^^^^^^^^^^
Error: This expression has type
         (string -> unit, string -> unit) CamlinternalFormatBasics.precision
       but an expression was expected of type
         (string -> unit, int -> 'a) CamlinternalFormatBasics.precision
       Type string is not compatible with type int
#