I'm replacing my kitchen faucet and the new faucet has 3/8" fittings on the hot/cold hoses, but the shutoff valves have 1/2" openings. Would it be better to replace the shutoff valves, or find an adapter like this?
In this case it would be a lot better to just replace the shut off valves, by adding an adapter you are just adding one more thing to break or go wrong and cause leaks! -7 years plumbing experience and red seal certified (Canada)
Use the adapter. Why go through all the trouble of installing a new shutoff, if you don't have to.
If you're using any fittings that have rubber washers, don't over tighten them. The washer could be crushed, deformed, or pushed out of the way.