"What is the default installation folder for Windows 2003 server?"
The default folder name is WINDOWS, but the user can input whatever name they like. There is no default partition so the drive letter could be anything in the range C to Z.
"In case if NT based OS use C:\WINNT as default, then why Windows XP (which is NT based) and even the Windows 2003 server at my office installed at C:\WINDOWS by default?"
The drive letter had no default in NT either so it might be D:\WINNT or Z:\WINNT or whatever, depending on which drives had which partitions and which partition the person was installing NT into.
As for why the default folder name changed, you'd really have to ask Microsoft, but here's my guess. Windows 2000 was supposed to unify the old NT series and old Windows 1/2/3/95/98 series, so there was no longer a need to distinguish the NT series, and they just defaulted the name to WINDOWS. My guess is that this plan assumed ME wasn't going to happen.
Anyway, in NT too, the person could type a different folder name if they didn't want the default folder name.