I think PH and Appsumo are not alternatives to each other.
If you have a Saas product, I think both should be tried. I think Appsumo is invaluable for early stage products. It means money for marketing and product development. I think it is valuable to generate income from the customer at 0 cost without making any investment.
It is possible to be very successful in PH with the community you will earn from Appsumo.
So I think PH and Appsumo should try for every Saas product.
Well, Product hunt is much more flexible.
Appsumo forces you into live time deals, which can be a double edge sword: https://www.lunadio.com/blog/the...
Product hunts offer you the option to run promotions but it doesn't"t have to be LTD. You can offer a discount on a subscription to boost your MRR.