Accelerated failure time models encompasses a wider range of survival time distributions than the proportional hazards model (Wiki page).
Although in principle any non-negative distribution can be used, the log-logistic distribution is most popular. This is similar in shape to the log normal but has heavier tails.
The lognormal, gamma and inverse Gaussian are also used.
The fact that the survivor and hazard functions for the lognormal can only be expressed in terms of integrals limits its usefulness.
The gamma distribution is quite similar to the Weibull. In fact, the generalised gamma distribution includes the Weibull and lognormal as special cases.
The inverse gamma has a rather complicated survivor function.
One limitation of the distributions used in the proportional hazards model is that they are monotonic in time, which may not always hold. A unimodal hazard function may be more appropriate in some cases.
