This is how I think of it. A double bond is electron deficient, hence lower pKa. A triple bond is more so, and an even lower pKa. Carbons are electron donors and therefore stabilize a double bond. Double bonds can have 4, 3, 2, 1, or 0 carbons attached. to them. You can find a table in your textbook showing you the stability order. In the two compounds being compared, one is mono substituted and the other disubstituted. The disubstituted is the preferred product.
I don't agree with blackzoid. Under SN1-like conditions (polar protic solvents), then the hydrogen of the more substituted carbon become more acidic (because of the electrons being attracted to the carbocation). This is like a hyperconjugation effect. As far as acidity is concerned, then methane>primary>secondary>tertiary. This is also consistent with carbon being a better electron donor.