Context: IGR J16479-4514 is a fast X-ray transient known to display flares lasting typically a few hours. Recently, its counterpart has been identified with a supergiant star, therefore the source can be classified as member of the newly discovered class of Supergiant Fast X-ray Transients (SFXTs), specifically it is the one with the highest duty cycle. Aims: to characterize the quiescent X-ray behaviour of the source and to compare its broad band spectrum to that during fast X-ray flares. Methods: we performed an analysis of IBIS and JEM-X data with OSA 5.1 as well as an analysis of archival Swift/XRT data. Results: we present results from a long term monitoring of IGR J16479-4514 with detailed spectral and timing informations on 19 bright fast X-ray flares, 10 of which newly discovered. We also report for the first time results on the quiescent X-ray emission; the typical luminosity value (about 10^34 erg s^-1) is about 2 orders of magnitude greater than that typical of SFXTs while its broad band X-ray spectrum has a shape very similar to that during fast X-ray transient activity, i.e. a rather steep power law with Gamma=2.6. Conclusions: IGR J16479$-$4514 is characterized by a quiescent X-ray luminosity higher than that typical of other known SFXTs but lower than persistent emission from classical SGXBs. We suggest that such source is a kind of transition object between these two systems, supporting the idea that there is a continuum of behaviours between the class of SFXTs and that of classical persistent SGXBs. ; Comment: 5 pages, 4 figures, accepted for publication in A&A