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What are the main differences? Advantages/disadvantages for both? What should they be used for?

the main difference today is that the one is no longer developed(mb3d) while the other is extending its dev team(mandelbulber)

From my POV - as one of very few using both programs - the following:

m3d has a "navigator", that's capable not only to navigate. It is also used as real time tweak tool (all formula params in all slots and many more can be manipulated with real time response). Mandelbulber has nothing similar.
IMHO this is the main reason for the popularity of m3d.
Further pros of m3d:
optimized quasi monte carlo renderer for hi quality renders with aa, realistic dof including depth Bokeh. Additionally mc renders can be interrupted, saved and loaded for later continuing.
Mandelbulbers mc rendering is unbearably slow with only a fraction of functionality.
m3d has a very fast volumetric light. Mandelbulber's vol light is very slow and meanwhile crippled in quality control. Dunno really when, but somewhere in v1 Buddhi removed the quality control value of vol light.
m3d has a direct mesh generation. don't use it for now, as for me 3d printing does not match the possible detail.

The main drawback of m3d: 32 bit app and therefor limited image size. The Big render module is only a weak compensation.

Pros of Mandelbulber:
Better quality in standard renderer even with ssao and faster rendering in single formula fractals. Map based ao that gives very good results at the cost of far slower rendering. Still it is faster, than any monte carlo renderer.
Better keyframe animation module with different interpolation modes, that all meet the exact state of keyframes. The quadratic bezier of m3d never reaches the keyframes exactly, which makes animations to some sort of lottery. Linear interpolation is angular and no alternative in most cases.
Additionally I use the keyframe animation in mandelbulber as half automated parameter search. With the know how, you can save the parameters of any frame calculated in your animation.

Theese are the points, that come to my mind for now. It's my observation as a user with almost no clou about the algorithms used.
My fave is still Mandelbulber especially when it comes to animations. I use m3d for some special hybrid still frames and sometimes for the mc renderer.

Hi Neosettler

M3D uses CPU
MandelbulberV2   uses CPU, and dev version V2.12 also has an openCL GPU option.  (old Mandelbulber V1.21 also has openCL option but is limited to single precision floating point)

When both programs are using CPU double  precision floating point  then the level of detail I would think should be the same , but I am not certain.

Many of the formulas in MandelbulberV2 have the same or similar maths to  M3D, so any difference would have to be in the engine

Engine. I do not know enough about this aspect to comment.

Formulas. M3D has a larger amount of formulas to choose from and lots of example settings on the Internet.

Users.  There are not many Mandlebulber users compared to M3D and a lot of MandelbulberV2 functions have only been implemented in the last two years.  The gallery at FF is full of my work which  is mainly a record of the formulas being implemented ( i am an explorer not an artist).  For artistic use of the program look for the work by user Taurus.  With M3D there are a lot of artistic users.