Is a Linux-based operating system really more powerful than one based on Windows NT?
What do you mean by more powerful, and what do you mean by Windows NT? XP, Vista, and Windows 7 are the spiritual successors of NT, but Windows NT as a named OS has been obsolete for about a decade, so modern Linux is more powerful simply by virtue of being more modern.
More powerful is a term for hardware when thinking about performance. You probably mean which has less of a performance setback. I'd say Linux because it can be customized heavily. For example, Windows' GUI is stuck to the non-graphical components whereas with Linux, the GUI and command line are separate entities and it's just a whole bunch of programs that work together and not one monstrous entity as in the case of Windows. Also, consider the fact that Linux only gets the dependencies it needs (for programs in repositories - which is most if not all of what you need and use) so it even uses less hard drive space. Using less hard drive space means the filesystem can better "focus" on eliminating fragmentation, as another example, since having less hard drive space means a file might need to be split if there is not enough space to save a file contiguously (=all in the same place). This is less important for solid state drives since access times are really low but for hard drives, it's a big deal. In short, Linux gives you a huge amount of control and you can use this to prioritize performance (or whatever else depending on your needs). For example, choosing to not have a GUI or choosing one that runs on 16MB of RAM or less, etc. This probably also is true for other operating systems such as Unix and BSD (with their userlands - aka the programs that come with a kernel such as the GNU programs that come with the Linux kernel in the case of GNU/Linux).
Powerful is a relative term in this situation. Linux and Windows are different approaches to the same problem and have strength and weakness in many aspects. It would depend on what purpose or application you are trying to achive.
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