E2 reaction — which one is faster?
For the E1 pathway, molecule A will react faster since the intermediate is more stable than from molecule B. According to this web site, the major product for A is 1,2-dimethylcyclohexene; for B, it is 1-methylcyclohexene.

For the E2 pathway, both reactions will have nearly the same rate. Depending on the orientation of the α-methyl group (cis or trans to Br), the major product is the same for cis, but for trans it will be 2,3-dimethylcyclohexene for A and 2-methylcyclohexene for B.