The tet10 is a "high order" element tet4 is a linear element the brick is a linear element. For a certain geometry you need more tet elements then bricks. The brick model will have therfore less DOF for the same accuracy. The tet4 is very stiff element and you need many of them to get good values for stress. When using tets always use tet10 (more nodes and DOF). Automatic meshing is easy with tets but more complex with bricks not every mdoel can be meshed with bricks (usually requires more work). Hope this helps...

Roni Plachta
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Roni's description is very good, but I will add to it with a little history.
Certainly it is much easier with today's modeling programs to automesh tets than it is to gain an equivalent mesh of bricks.  
There are two things which drove bricks meshing in the past: 1) as Roni pointed out, fewer DOF gives equivalent answers; and 2) the programs which automesh tets were not as robust in the past as they are today.
The incredible advances in computing power over the last decade have largely made item 1 a moot point--many of the more powerful PC's are able to do the same work that only recently required a supercomputer.  As such, what was once a 10,000 dof brick model can be made into a 100,000 dof 2nd order tet model, and still be run on a pc or a desktop workstation.
Along with this advance, many preprocessors have made huge strides in tet automeshing, which has now made it equivalently much more efficient (from a human modeling standpoint) to model tets (vs. modeling bricks) than it once was.
Depending on the type of analysis one is doing, there are still benefits to modeling bricks sometimes, instead of tets.  However, for general purpose (especially linear, small-displacement), if your computer can handle the dof's, it is generally much less headache and man-time to model tets.
Historically, this wasn't always the case, hence the tradition of bricks.

Apologies that the constant strain/stress aspect of 4-noded tets was not explicitly stated.  It was implied in Roni's description, but probably only for those who already knew the answer. I would take exception to one statement Javier made. He recommended using "a very fine mesh of 4-node tetrahedrons" in certain situations.  I would strongly discourage that, unless it is absolutely the only option.  Second order tets do not exhibit the strain locking which occurs in first order tets, and an equivalent d.o.f. model of second order tets will give a more accurate answer than that given by first order tets.  By definition, most of the time peak stresses occur in relatively high-gradient areas.  These are the very areas in which 1st order tets are at their worst.  
First order tets ultimately will converge to the "correct" solution, but not nearly as quickly as 2nd order tets do.  Their convergence is poor enough that many FEA software manufacturers state that they in fact should not be used unless absolutely necessary.
One other issue that I failed to mention before: 1st order fully integrated brick elements also exhibit shear locking, and can give poor results in bending.  For this reason, again second order tets generally give superior results (I make this generality while acknowledging that this is not always the case).
A few years back I actually lead an extensive study into this very question, and our ultimate conclusion was that we should use second order tets (at the time, we were using first order brick elements). For general purpose considerations, they were superior.