Purpose: To investigate the coupling of radiobiological models with patient-specific Monte Carlo (MC) dose calculations for permanent implant prostate brachytherapy (PIPB). To compare radiobiological indices evaluated with different radiobiological models using MC and simulated AAPM TG-43 dose calculations. Methods: Three-dimensional dose distributions previously computed using MC techniques with two types of patient models, TG43sim (AAPM TG-43 water-based conditions) and MCDmm (realistic tissues and interseed effects), for 613 PIPB patients are coupled with biological dose and tumour control probability (TCP) models. Two approaches and their extensions are considered to evaluate biological doses, biologically effective dose (BED) and isoeffective dose (IED), as well as two methods to evaluate TCP. Three novel extensions of equivalent uniform biologically effective dose (EUBED) are suggested which consider the spatial distribution of doses within the target volume. Adopted radiobiological model parameter values (a, b, etc) are those suggested by AAPM TG-137, and sensitivity to parameter choice is discussed. Results: MCDmm dose calculations can reveal low doses in the prostate target volume, due to tissue heterogeneities or inter-seed effects; considering these low doses in EUBED calculations can lower TCP estimates by up to 70%, with largest differences in patients with calcifications. There are large variations in biological doses and TCPs evaluated over the 613 patient cohort for each radiobiological model considered, reflecting the spectrum of physical doses calculated for these patients with either MCDmm or TG43sim. Depending on the model details, BED, IED and EUBED are, on average, 6.0-9.8%, 7.4-9.2% and 1.8-15% higher, respectively, with TG43sim than MCDmm. TCP estimates computed using MCDmm dose distributions are much lower than expected based on past treatment outcome studies, suggesting a need to re-assess model parameters when evaluating radiobiological indices coupled with heterogeneous tissue model-based dose calculations. Conclusions: Cohort average differences in biological dose and TCP estimates between radiobiological models are generally larger than differences for any one radiobiological model evaluated with TG43sim or MCDmm dose calculations. However, heterogeneous tissue dose calculations, like MCDmm, can identify clinically-relevant low dose volumes, e.g., in patients with calcifications, which would otherwise be missed with TG-43. In addition to affecting physical dose distributions, these low dose volumes can largely impact radiobiological dose and TCP estimates, which further motivates the clinical implementation of model-based dose calculations for PIPB.