Which toolset is better to use?

I am wondering how I can choose a good AVR8 compiler for the Arduino-ide
There are two toolsets for this purpose:

1- WinAVR (Obs. after 2011)
2- AVR-GCC toolset available on Atmel website

I want following features:
(a) Better+faster compilation with smaller code size
(b) Better support for C++ programming and support for C++11 standard

(c) iostream, and many C++ standard headers (highest compatibility) I know the environment
is very limited but I want to choose a compiler with maximum compatibility

I have no idea why the header files bundled with the windows version of AVR-GCC(Atmel) does not contain any standard headers!

I am confused on how can I use iostream in those AVR-GCC(Atmel) compiler, is there any need for extra tweaking components that are either missed or disabled.

Thanks

Better and faster ? The Arduino uses the avr-gcc compiler. You can add extra compiler options. The Arduino optimizes for size, you can change that in the file "platform.local.txt". It is possible to add the compiler option "-flto", you can't get better than that.

Is there a problem with the C++ in the Arduino IDE ?

iostream headers are used for a program on a computer. A microcontroller is a microcontroller, and doesn't have all that input and output. Do you want the default output to be printed to the serial monitor ?

Perhaps the Raspberry Pi is what you want. That is a linux operating system.
Or perhaps the Arduino Yun, that is a Arduino Leonardo with a wifi/linux/OpenWRT module.

The most common Arduino is the Arduino Uno board. It uses the ATmega328P microcontroller. That is a microcontroller, which can do timing, sequences, read and write pins, and so on. It is not a computer.

Winavr is just an older version of avr-gcc, and it doesnt support many of the newer atmel chips. So I don't really think it should be used any more.

Afaik, any c++ library you want to use will need to be downloaded separately from somewhere else. Avr gcc only includes a c runtime library.
Avr-libc is also maintained separately, by somewhat different people, than gcc itself.