The models are equivalent. In Method 1 you use the superposition principle of Poisson processes. The sum of all unique arrival rates will be the total arrival rate.
In Method 2 you first look at this total arrival rate and use thinning to get processes with the individual rates.
In both cases the time to next arrival is Exp(lambda), where lambda is total arrival rate. Also, the probability that the next arriving party is of size n is
(rate party size n)/lambda