There are two 319 variants, the Airbus Corporate Jet (ACJ) and 319LR. They're pretty similar though the ACJ is more expensive.
There are two BBJs: BBJ1 and BBJ2 one is a 700 the other an 800 although the 700 is a hybrid, and has 800 wings.
Then there is the 737-700ERX and 737-800ERX. The 737-700ERX is most comparable to the 319LR, but it flies further.
The 319 is wider, but also heavier, so the range is often the winner for the 737 for private/ state aircraft.
Overall they are similar concepts: standard aircraft, structurally enhanced with added fuel tanks.