while true do
      io.write "1"
    end

PUC-Rio 5.4: 25 MiB/s

LuaJIT 2.1.0-beta3: 550 MiB/s <--- WOW

They all go slightly faster if you localize the reference to `io.write`

    local write = io.write
    while true do
      write "1"
    end

No noticeable difference for LuaJIT, which makes sense, since JIT should figure it out without help.

5.1 and 5.4 show about ~8% improvement.

    main = putStr (repeat '1')

Strings are printed one character at a time in Haskell. This choice is justified by unpredictability of the interaction between laziness and buffering; I am uncertain it's the correct choice, but the proper response is to use Text where performance is relevant.

  poll([{fd=1, events=POLLOUT}], 1, 0)    = 1 ([{fd=1, revents=POLLOUT}])
  write(1, "11111111111111111111111111111111"..., 8192) = 8192
  poll([{fd=1, events=POLLOUT}], 1, 0)    = 1 ([{fd=1, revents=POLLOUT}])
  write(1, "11111111111111111111111111111111"..., 8192) = 8192

  poll([{fd=1, events=POLLOUT}], 1, 0)    = 1 ([{fd=1, revents=POLLOUT}])
  write(1, "11111111111111111111111111111111"..., 8192) = 8192
  rt_sigprocmask(SIG_BLOCK, [INT], [], 8) = 0
  clock_gettime(CLOCK_PROCESS_CPUTIME_ID, {tv_sec=0, tv_nsec=920390843}) = 0
  rt_sigprocmask(SIG_SETMASK, [], NULL, 8) = 0
  rt_sigprocmask(SIG_BLOCK, [INT], [], 8) = 0
  clock_gettime(CLOCK_PROCESS_CPUTIME_ID, {tv_sec=0, tv_nsec=920666397}) = 0
  ...
  rt_sigprocmask(SIG_SETMASK, [], NULL, 8) = 0
  poll([{fd=1, events=POLLOUT}], 1, 0)    = 1 ([{fd=1, revents=POLLOUT}])
  write(1, "11111111111111111111111111111111"..., 8192) = 8192

I'm also not sure what's going on in the second case. IIRC, at some point historically, a sufficiently tight loop could cause trouble with handling SIGINT, so it might be related to some overagressive workaround for that?