Pedantic, but important: the title is wrong, it is showing linux distribution flavors, not linux flavors. As other posters point out, the different distribution flavors have different mixes of packages and versions.
The biggest advantage of the Debian (and derived) distributions is that they have the largest set of prepackaged "things," which makes most things an "apt-get" away. This is very convenient, but not essential.
Back to your question, prepackaged "things" must be installed on the distribution that prepackaged it (you can "cross the streams" to some extent, but a cross-distribution install has a finite, possibly large, probability of not running).
If you are willing to build the "thing" itself, the portability is pretty close to 100% that it will Just Work[tm] with a "configure && make" build. For complex "things" with dependencies, this can grow geometrically into being a major effort to find and build all the dependencies.
The biggest advantage of the Debian (and derived) distributions is that they have the largest set of prepackaged "things," which makes most things an "apt-get" away. This is very convenient, but not essential.
Back to your question, prepackaged "things" must be installed on the distribution that prepackaged it (you can "cross the streams" to some extent, but a cross-distribution install has a finite, possibly large, probability of not running).
If you are willing to build the "thing" itself, the portability is pretty close to 100% that it will Just Work[tm] with a "configure && make" build. For complex "things" with dependencies, this can grow geometrically into being a major effort to find and build all the dependencies.