You need to check what each card offers. If you have two choices to buy an airline ticket on say United and your choices are

Pay with an American branded card and get one American mile per dollar

or

Pay with a United branded card and get 3 miles per dollar (depends on the card)

you have to decide which miles are more important to you. Same thing with hotels, etc.

Remember though you need to get enough miles to actually use them (well at least I believe that's true, some people just like collecting) so if you pile up a few here and a few there and some here and some there you may never get enough anyplace to actually make it worth the effort. You need to balance the added rewards of another card against the chance you may not be able to use those miles later.