Several simple dark energy models on the brane are investigated. They are compared with corresponding models in the frame of 4d Friedmann-Robertson-Walker cosmology. For constraining the parameters of the models considered, recent observational data, including SNIa ap- parent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter den- sity perturbations are used. Also, explicit formulas of the so-called state-finder parameters in teleparallel theories are found that could be useful to test these models and com- pare Loop Quantum Cosmology and Brane Cosmology. The conclusion is reached that a joint analysis as the one devel- oped here allows to estimate, in a very clear way, possible deviation of our cosmology from the standard Friedmann- Robertson-Walker one