Both were designed in the middle of a war with the sole aim of producing the best anti tank gun they could and bring it into service ASAP. HE or smoke rounds were niceties.
British "doctrine" tended to favour single role weapons. So the 6pdr AT gun was designed to be used as an Anti tank gun or fit tanks designed for killing tanks. 1941/2 doctrine still had a number of Close support tasnks with howitzers for use against dug in targets.
The British didnlt think there was any point in having small calibre HE so never bothered for the 6pdr, whereas the Germans had He for their 50mm equivalent.
There were Chemical Shelll developed for the 2/6/17 ATK Guns. The problem was they were experimental and being direct fire weapons they looked like - Proof Shot! Deep joy ploughing around former P&EE's
However I also seem to recall that all of the variants of these guns had HE rounds of some sort.