Nail trimming blunts the nails so they do less damage, while Soft Paws are little vinyl nail caps that cover the nail, so the nails cannot scratch at all.
My first recommendation is usually nail trimming, because it's simpler & less expensive than using soft paws. But if that isn't sufficient (say for people with very thin skin that is easily scratched, or with cats that destructively scratch furniture), I recommend trying soft paws. I used them on my cats for several months to avoid damage to the furniture while I trained them not to scratch & refocused them on acceptable scratching surfaces. Now that they're pretty good about not trying to scratch the furniture, I just trim the nails, & save the soft paws in case they relapse.
If you want to try soft paws, read the application instructions carefully before using, as pointed out by Russian Blue. Also, it's very important to note that because soft paws completely blunt the cat's claws, it's important to keep cats with soft paws on indoors.
Hope this helps.