I had always stayed in Irún until this last summer, when we decided to start in Hondarribia. Hondarribia is a much nicer stay. Irún is a lively enough town; there are plenty of shops and bars. There's nothing particularly noteworthy about it otherwise, though, at least that's my experience. Hondarribia is lovely--you've got a decent beach just out of the center, a fantastic plaza in the center of the hill town, with sweeping views, and still plenty of places for food/supplies. Plus, since you're coming directly into Hondarribia, going back into Irún would add some unnecessary kms to your walk.
The best arguments to be made for Irún are price (you could stay in the albergue there for much, much less than whatever your accommodation in H would charge) and pilgrim community (far, far more pilgrims start there, so it's a better place to start making social connections). Those might make the kms worthwhile, depending upon your interests.