I realize this is an older question, but in case anyone is still interested, I briefly will try to add my own thoughts on your question:
What are the main differences between them? What are the advantages and drawbacks of each of them with respect to the other one?
In my view, the main difference is a substantially higher degree of customizability of TeXstudio in comparison to Texmaker.
This one aspect captures, in my opinion, the most important difference between the two programs. And to me at least, this aspect was also the main factor in choosing one over the other.
I don't know anything about the forking circumstances of TeXstudio, i.e. whether the TeXstudio devs followed forking etiquette or not (as suggested above in a comment). But as far as the current program is concerned, for the customizability reason mentioned above, I much prefer working with TeXstudio ever since I found out it exists -- which actually took a while, since it seems that it's not nearly as famous as Texmaker.
I'll give two examples where customization differs -- two small things that always bothered me in Texmaker, and that just instantly disappeared when switching to TeXstudio:
Disabling the sidebar/side panel. Both programs show, by default, a sidebar menu containing commonly used commands, e.g. an "italics" button, and so on. However, I prefer to maximize my available screen space, so would rather not see that menu. In Texmaker, this menu can't be removed (at least, last timed I checked). In TeXstudio on the other hand, you can show/hide it. Small detail, but to me it actually mattered.
Fine-tuning autocomplete commands. In Texmaker, you can add your own commands to the list of autocomplete commands, and there's a list of existing commands that you can edit, i.e. remove commands from the list. But: for some reason, no idea why, there are a few commands that are always suggested, and sometimes in an order that really didn't work well for me (e.g. \citep is always suggested, before \cite). Never found a way to change at least the order in Texmaker, but immediately could change it in TeXstudio.
Other than the issue of customization, the two programs are very similar. TeXstudio has a slightly "brighter" looking standard UI, but I can't say I like it better than the texmaker UI.
In summary, I think your choice between Texmaker and TeXstudio should depend on whether you ever thought that Texmaker offers a too little options/is a bit short on customizability. If not, I'd say go with Texmaker, since it's still the 'standard' as far as I can tell. If, on the other hand, there have been some (minor or major) things that keep nagging you in Texmaker, I highly suggest to give TeXstudio a try.