Step 1: Recall the Solow model.
In Solow's model growth comes from capital, labour and technology, but the technology improvement is taken as given from outside. So it is exogenous there.
Step 2: Recall the Romer model.
Romer builds growth from inside, through research, innovation and the spread of knowledge. So in his model the engine of growth is endogenous.
Step 3: Check option A.
Solow usually assumes constant returns to scale, not increasing returns. So A is wrong.
Step 4: Check option B.
The long run growth driver is exogenous in Solow and endogenous in Romer. This is the heart of the difference, so B is the correct statement.
Step 5: Knock out C and D.
Solow does include technical progress, just from outside, so C is wrong. Romer's growth is not exogenous, so D is wrong.
\[ \boxed{\text{Exogenous in Solow, endogenous in Romer}} \]