By using three-terminal double tunnel junction devices at 2.2 K we have injected quasiparticles into epitaxial thin films of niobium and tantalum. The two junctions are coupled by quasiparticle diffusion and the diffusion of recombination phonons through the sapphire substrate. A comparison of our experimental results with a random walk simulation of the quasiparticle diffusion process enabled us to estimate the lifetime of the injected quasiparticles. The quasiparticle lifetime is not recombination limited in epitaxial Nb and Ta films. Furthermore Ta is less susceptible to the (as yet undetermined) loss mechanisms which govern the quasiparticle lifetime. This result indicates that tunnel junction particle spectrometers utilising Ta absorbers may display better energy resolution than those with Nb absorbers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>