But that flow rates are still equal. Is this true? If connecting pex and copper should I use a wider piece of pex?
1/2" pex is about the same ID as 3/8" copper...it all depends on what you're feeding with that pipe/tubing run. A run for a faucet can use 1/2" pex. A tub would be underwhelming - the flow rate would be restricted in most cases but would be fine for one showerhead. Then, the longer the run, the more friction. Pex is ideally run with few if any fittings except at the beginning and end of the run...copper would often require lots of fittings since it doesn't ben around corners. Each fitting also slows the water down from internal friction. So, it depends. But for maximum volume capability, you need to put in larger pex than the equivalent copper supply line. The ID and ODs are all available easily on a search. My comments are generic, but all pex is within a very small margin of those numbers.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013