This is how I think of them. Elimination reactions can be thought of as push-pull reactions. If the leaving group leaves before the proton is lost, the carbocation (and leaving group) pull electrons toward it. These reactions give the more substituted alkenes because the carbon or hydride best able to donate electrons is the more substituted.
In a pull reaction, the leaving group does not make the same contribution. In order for the reaction to occur, it is acidity of the hydrogen that dominates the products. So poor leaving groups and poor conditions for carbocation formation favor Hoffman products.
This reaction is difficult to predict and probably difficult to get a large degree of selectivity because bromides are such good leaving groups. If you had the chloride, then I'd think the Hoffman product would be in a larger ratio. In this case, I think the Hoffman product will be major, but with an appreciable amount of the Zaitsev product.