The methyl group is bulky and so is most stable in the equatorial position.
The 1,4 cis compound's most stable chair form has its leaving group (Br) and beta-hydrogen in an anti-coplanar (anti-periplanar in some textbooks) conformation.
So most of the time, 1,4 cis is in a chair conformation that is able to undergo an E2 reaction.
The opposite is true for the 1,4 trans compound. Most of the time it is in a chair conformation that is unable to undergo an E2 reaction.
Therefore, the 1,4 cis compound will undergo an E2 elimination reaction faster than the 1,4 trans compound.
