Why quaternary nitrogen but not tertiary oxygen?

Why do [quaternary ammonium ions](https://en.wikipedia.org/wiki/Quaternary_ammonium_cation) with a partially positive nitrogen form fairly readily and are often stable but tertiary oxygens, apparently called [oxonium ions](https://en.wikipedia.org/wiki/Oxonium_ion), are more rare/less stable? The trend seems to continue down the periodic table, too, with phosphonium and sulfonium.




This has to do with the electronegativity of the species and how good of a base (or how good an acid the conjugate acids) are.


$\hspace{9ex}$ [![H3O+](https://i.stack.imgur.com/TJiMn.png)](https://i.stack.imgur.com/TJiMn.png)


$\hspace{7ex}$ [![enter image description here](https://i.stack.imgur.com/Bp3GQ.png)](https://i.stack.imgur.com/Bp3GQ.png)


[[source](http://cactus.dixie.edu/smblack/chem2310/summary_pages/pKa_chart.pdf)]


To put this in perspective, nitric acid ($\ce{HNO3}$) has a $\mathrm{p}K\_\mathrm{a}$ of $-1.3$. Yes, $\ce{HNO3}$, a strong acid, is more stable than $\ce{H3O+}$! The central oxygen in $\ce{H3O+}$ is too electronegative to effectively share these electrons and form a stable bond. In $\ce{NH4+}$, its lone pairs are far more available due to nitrogen's lower electronegativity. 


How common each species is only has to do with the number of acids stronger than $\ce{H3O+}$ or $\ce{NH4+}$. As you can imagine, there are going to be a lot more acids stronger than $\ce{NH4+}$, which starts out around the middle of the $\mathrm{p}K\_\mathrm{a}$ spectrum, than compared to $\ce{H3O+}$, which is near the end.


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The electronegativity of Oxygen is higher than Nitrogen, so it is much less suited for holding a positive charge, which, in turn leads to Mithoron's comment about weaker nucleophilicity and better leaving group ability.


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