So if your borders intersect with his, you'll get an additional +1 from liberating cities and a guaranteed open borders. If you gift any old city, you just get the standard +4.
So because of the 3 tile rule, you'll generally have to plant a city next to one of his that have border popped once.
If you can get a barb city to raze it, that's good, but even better is if it you place it between his borders and another AI's borders, to spark tension.
Also, you can try to plant it to mess up his settling patterns, so it's impossible to grab say a gold due to city proximities.