The relationship between Aeneas and Dido is a complicated one, especially because it was set in motion by the goddess Venus, who wanted to ensure her son Aeneas' glorious future. Thus, when Aeneas is shipwrecked at Carthage, Venus makes Dido fall in love with Aeneas (see Aeneid 1).
In Aeneid 4, the bond between Aeneas and Dido is further strengthened when Venus and Juno arrange for Aeneas and Dido to consummate their relationship in a physical way. Thus, Juno says, "I’ll join them firmly in marriage" (A.S. Kline translation).
The text, however, makes it clear that Dido was more keen on the relationship than Aeneas was. She is the one who was "wounded long since by intense love" (Aeneid 4.1).
So, I would probably say that Aeneas' attraction to Dido was primarily physical. Vergil, however, is rather silent about how Aeneas feels about Dido.
This relationship is also complicated by the historical allegory behind it. Vergil's Roman audience would have noticed parallels between Aeneas and Dido and Julius Caesar and Cleopatra and Marc Antony and Cleopatra. These pairings of Roman male and African female, as Vergil's audience knew, were doomed to fail. Furthermore, Vergil's audience would recall their long-time hostility with the Carthaginians and would know that such a relationship as that between Dido and Aeneas was not sustainable.