Regarding the kingdom Animalia, which phylogenic tree is more common: Molecular Comparisons or Body-Plan Grades
Long story short, use sequence information if you can.

The long story long:
Sequence information and the trees generated from them are strictly more reliable than morphological characters. For instance: sharks are pretty much the same shape they were millions of years ago, but they've been accumulating genetic differences 'invisibly' that allows us to group the different kinds of shark accurately. Where genetic data is unavailable (paleontology as a rule, certain kinds of field taxonomy where it's cheaper to code the morphological features of each new beetle than sequence them all) morphological trees are still used. So in terms of which tree type is more common: It depends.

In terms of which tree type is more accepted, it's genetic data by a landslide. Genetic data by and large is much less affected by homologous structures and convergent evolution. In addition, it works on species that all look pretty much identical (imagine trying to code hundreds of bacterial species that are all closely related). Using highly conserved cellular machinery, trees for very distant species can be constructed. Using unconserved noncoding sequences trees for very closely related individuals trees can be constructed with a reasonable degree of accuracy.

Some examples: Mitochondrial Eve would be impossible to date with morphological characters. There's just not enough morphological variation between humans.
Opabinia is a really good example of how hard it is to classify things based on shape, especially when they're a weird shape.
Something you can do yourself: Human  and Thermodesulfator(seq) are about as morphologically distinct as two living things can be. One is you, and one eats carbon dioxide and breathes sulfate and hydrogen. It lives at the bottom of the sea and would be more at home in a cup of hot coffee than outside it. Nevertheless, the two species show ~50% sequence similarity using 16S, twice as much as would be expected by chance and easily enough to classify a third thing as more closely related to one or the other. Try it yourself if you like.