On a moderately loaded Solaris machine, alias keeps ahead of ref, but it seems that the string length dominates the speed, as both rates get lower and closer to each other with no signs of one overtaking the other:

Length of string: 1000
          Rate   ref alias
alias 141243/s   58%    --
ref    89366/s    --  -37%

...

Length of string: 10000
         Rate   ref alias
alias 45496/s   19%    --
ref   38388/s    --  -16%

...

Length of string: 20000
         Rate   ref alias
alias 25947/s   12%    --
ref   23186/s    --  -11%
[download]

This is for

This is perl, v5.8.4 built for sun4-solaris-64int
(with 27 registered patches, see perl -V for more detail)
[download]

On a different machine, also moderately loaded, I see practically the same, also with alias keeping (barely) ahead of ref as the string size increases:

Length of string: 1000
          Rate   ref alias
alias 404858/s  115%    --
ref   187970/s    --  -54%

Length of string: 2000
          Rate   ref alias
alias 367647/s   87%    --
ref   196850/s    --  -46%

...

Length of string: 10000
          Rate   ref alias
alias 220751/s   24%    --
ref   177936/s    --  -19%

...

Length of string: 18000
          Rate   ref alias
alias 168067/s    2%    --
ref   165563/s    --   -1%

Length of string: 19000
          Rate alias   ref
ref   162866/s    1%    --
alias 161551/s    --   -1%

Length of string: 20000
          Rate alias   ref
ref   162602/s    2%    --
alias 160000/s    --   -2%
[download]

Here, the decrease in repetitions is more dramatic for alias as the string length increases, which I interpret as the runtime overhead of alias being really minuscule compared to the overhead of the other operations performed.

This is on a HP-UX machine with Intel architecture:

This is perl, v5.8.8 built for IA64.ARCHREV_0-thread-multi
(with 33 registered patches, see perl -V for more detail)

Copyright 1987-2006, Larry Wall

Binary build 817.1 [268662] provided by ActiveState http://www.ActiveS
+tate.com
Built Sep 19 2006 13:53:03
[download]

Interestingly, trying this with Strawberry 5.10.0, I see your reversal (Intel architecture):

          Rate   ref alias
ref   258065/s    --  -46%
alias 477783/s   85%    --

...

Length of string: 10000
          Rate alias   ref
alias 123533/s    --  -25%
ref   164528/s   33%    --

...

Length of string: 20000
          Rate alias   ref
alias  65509/s    --  -42%
ref   112867/s   72%    --
[download]

This is for

This is perl, v5.10.0 built for MSWin32-x86-multi-thread
[download]

Trying on the same machine with Strawberry 5.8.8, I get

Length of string: 1000
          Rate   ref alias
alias 511771/s   53%    --
ref   335121/s    --  -35%

Length of string: 2000
          Rate   ref alias
alias 383289/s   28%    --
ref   299043/s    --  -22%

Length of string: 3000
          Rate   ref alias
alias 318471/s   14%    --
ref   279486/s    --  -12%

Length of string: 4000
          Rate   ref alias
ref   256016/s    --   -2%
alias 262329/s    2%    --

Length of string: 5000
          Rate alias   ref
alias 219154/s    --   -7%
ref   236183/s    8%    --

...

Length of string: 10000
          Rate alias   ref
alias 121448/s    --  -29%
ref   170707/s   41%    --

...

Length of string: 20000
          Rate alias   ref
alias  67801/s    --  -39%
ref   111694/s   65%    --
[download]

This was with:

This is perl, v5.8.8 built for MSWin32-x86-multi-thread
[download]

So, at least judging from the limited set of versions and platforms, things point in the direction of Windows or MSVC to be responsible for the dramatic slowdown although I'm at a loss as to what part might be causing the slowdown.