#1 - The 33BM has a newer CPU (Core i3-7100u) with a graphics core (the Intel HD 620) that is probably around 15% - 20% more powerful than the Intel HD 520 in the 31KW model.
#2 - The 33BM has a backlit keyboard. The slightly older 31KW does not.
I recommend you install a second stick of RAM to improve graphics performance probably by another 10% - 15%. Two sticks means the RAM is operating at full speed rather than half speed which would slow down the graphics core.
The Intel HD 620 is pretty much the best graphics option you can get within your budget. Intel has basically caught up to AMD for integrated graphics. The only AMD graphics core more powerful than the Intel HD 620 is the Radeon R7 (Bristol Ridge) found in AMD's FX-9830p APU.