Energy distribution curves (EDCs) of laser-induced electron pulses from a tungsten tip have been measured as a function of tip voltage and laser power. Electron emission via tunneling through and/or excitation over the surface barrier from photo-excited nonequilibrium electron distributions are clearly observed. The spectral shapes largely vary with the emission processes and are strongly affected by electron dynamics. Simulations successfully reproduce the spectra, thus allowing direct insight into the involved electron dynamics and revealing the temporal tunability of electron emission via the two experimental parameters. These results should be useful to optimize the pulse characteristics for many applications based on ultrafast laser-induced electron emission.