Interesting concept

Had my second winning session in a row, and it was a monster. May have been easiest win ever, did all my damage in just over an hour. I am very excited to have a working bankroll, and an emergency bankroll going forward. I can definitely loosen up my calling ranges.

Interesting hand came about, with me and the super aggressive older gentleman that had a giant mound of chips, and didnt mind putting them in a pot.  He raised it up in early position for $40 from a $6 straddle two customers, I see AA and make it $140. Aggro calls. Flop coms QdQhJd and I shove all in for $400 he folds.

Now here's my question if you have conceded to playing the hand for all your chips, is it better to check and have your opponenet go all in, and call? or do you go all in?