Why does one awk go faster than the other?

gistfile1.txt

File is ~100 million lines, with ~30 categories in the first column. So sort type 1 should execute ~30 subprocesses.
Takes ~ 180 seconds, so subprocess overhead should be very minimal. 

Type 1, multiple sub-sorts:

$ time env time -v -o sort1.time awk -v cmd="sort -k2,2n" '$1 != prev {close(cmd); prev=$1} {print | cmd}' vcf.bed > vcf.sort1.bed  

real	2m57.867s
user	0m46.381s
sys	4m14.309s


Type 2, decorate sort undecorate:

$ time env time -v -o sort2.time awk '{print ($1 in a? c+0: ++c)"\t" $0; a[$1]}' vcf.bed | time -v -o sort2.sort.time sort -k1,1n -k3,3n | time -v -o sort2.cut.time cut -f 2- > vcf.sort2.bed

real	2m31.199s
user	0m24.973s
sys	2m14.660s


Surprisingly, (to me) the type 1 takes more realtime (+20%), AND more cpu time (+100%). 
More detailed /usr/bin/time -v reports below.

Things that stand out to me (type 1 vs 2):
    LOTS of page faults - mmap-ed io? (1135087 vs 301240)
    Less memory - (smaller sorts?) - 55052 vs 74472
    LOTS of context switches - un or line buffered io? - 28717559 vs 392500
    similar fs out calls , ~3 million
    
    
It would be nice to also get time on type 1 awk's child sort.
I could also ltrace awk to see how it does print | cmd...

gistfile2.txt

	Command being timed: "awk -v cmd=sort -k2,2n $1 != prev {close(cmd); prev=$1} {print | cmd} vcf.bed"
	User time (seconds): 46.38
	System time (seconds): 254.17
	Percent of CPU this job got: 169%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 2:57.61
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 55052
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 0
	Minor (reclaiming a frame) page faults: 1135087
	Voluntary context switches: 28717559
	Involuntary context switches: 559
	Swaps: 0
	File system inputs: 0
	File system outputs: 3356744
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0

gistfile3.txt

	Command being timed: "awk {print ($1 in a? c+0: ++c)"\t" $0; a[$1]} vcf.bed"
	User time (seconds): 5.71
	System time (seconds): 50.37
	Percent of CPU this job got: 42%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 2:11.39
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 5060
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 0
	Minor (reclaiming a frame) page faults: 7589
	Voluntary context switches: 124
	Involuntary context switches: 86
	Swaps: 0
	File system inputs: 0
	File system outputs: 0
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0
  
  
	Command being timed: "sort -k1,1n -k3,3n"
	User time (seconds): 18.32
	System time (seconds): 76.23
	Percent of CPU this job got: 62%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 2:31.18
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 74472
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 0
	Minor (reclaiming a frame) page faults: 301240
	Voluntary context switches: 392500
	Involuntary context switches: 342
	Swaps: 0
	File system inputs: 0
	File system outputs: 3845120
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0
  
  
 
	Command being timed: "cut -f 2-"
	User time (seconds): 0.92
	System time (seconds): 7.86
	Percent of CPU this job got: 5%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 2:30.89
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 4664
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 0
	Minor (reclaiming a frame) page faults: 4319
	Voluntary context switches: 39822
	Involuntary context switches: 58
	Swaps: 0
	File system inputs: 0
	File system outputs: 1680728
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0