It depends on the type of product. Clothes etc I usually shop on mobile. Larger/more expensive items (speakers etc) I usually compare on desktop. This is usually because it's quicker to switch between tabs and compare on desktop.
@benjidisciple thanks for your feedback. The version 2 of my app (https://www.mosc.app) will be a mix between universal online shopping cart and price comparator, that means you could search if an item added to your global cart is cheaper on another covered e-shop.