We present a new catalog and results for the cluster system of the starburst galaxy NGC 4449, based on multiband imaging observations taken as part of the LEGUS and H-alpha-LEGUS surveys. We improve the spectral energy fitting method used to estimate cluster ages, and find that the results, particularly for older clusters, are in better agreement with those from spectroscopy. The inclusion of H-alpha measurements, the role of stochasticity for low-mass clusters, the assumptions about reddening, and the choices of SSP model and metallicity all have important impacts on the age dating of clusters. A comparison with ages derived from stellar color-magnitude diagrams for partially resolved clusters shows reasonable agreement, but large scatter in some cases. The fraction of light found in clusters relative to the total light (i.e., T-L) in the U, B, and V filters in 25 different approximate to kiloparsec-size regions throughout NGC 4449 correlates with both the specific region luminosity, R-L, and the dominant age of the underlying stellar population in each region. The observed cluster age distribution is found to decline over time as dN/d tau proportional to tau(gamma), with gamma = -0.85 +/- 0.15, independent of cluster mass, and is consistent with strong, early cluster disruption. The mass functions of the clusters can be described by a power law with dN/dM proportional to M-beta and beta = -1.86 +/- 2, independent of cluster age. The mass and age distributions are quite resilient to differences in age-dating methods. There is tentative evidence for a factor of 2-3 enhancement in both the star and cluster formation rate approximate to 100-300 Myr ago, indicating that cluster formation tracks star formation generally. The enhancement is probably associated with an earlier interaction event.