I mean things like 2>&1 or 2>/dev/null (redirecting error stream to stdout etc). This did not work for me last time I tried it. This coupled with significant lag when scrolling/listing huge dir, typing made me quickly abandon it. Terminal app does everything I really need and it's fast and reliable.

These things have nothing to do with the terminal emulator you're using and everything to do with your shell.

  > I mean things like 2>&1 or 2>/dev/null
  > (redirecting error stream to stdout etc)

These things are usually handled by the shell...

Sure, but if I execute a command like

    `sudo find / -ctime 0 2>/dev/null` 

in both iTerm and Terminal side by side, I would expect them both to print out the same thing, but that was not the case.

cat a big logfile on iTerm, cat a big logfile in terminal.

Then for some really screaming performance, cat a big logfile in xterm. Then, for insane performance cat a big logfile in mrxvt or rxvt.

Anti aliasing really slows things down, so performance is faster in the "native" terminal apps when that turned off, but with x11, theres way less than millisecond delays for printing stuff on the screen. I do like my terminal to be fast.