Midscreen use A version to knock people down and push them towards the corner during combos. For example after
x 2 hitconfirm. The C version followed by Second Shoot is always guaranteed off of this regardless of range, mostly due to the speed of C version Second Shoot. However, since A knocks down, even if the Second Shoot doesn't combo, you can use it to knock them towards the corner and then force them to block the Second Shoot, allowing some pressure. Use C version midscreen if you are really desperate for the extra damage and you want to be absolutely sure.
The frame data on the wiki seems to indicate that both versions of Ein Trigger are the same on block (-5). Reiki, are you sure the A version recovers faster?