Depends on the average MMR of your team compared to the average mmr of their team, as well as your personal mmr compared to your division.
You almost certainly didn't have the same mmr for both games, so your lp losses/gains wouldn't nencessarily be the same between them. Also, having a plat on your team doesn't mean that you had a better player. By virtue of you being matchmade with them, it is very suggestive that they are are very poor plat player with an mmr around gold 5 (or you have an mmr better than gold 5, and you're meeting somewhere in the middle; point is you have similar mmrs).
Also if there were premades involved, you can have better than expected players in your game but also some worse than expected in the game, so the average mmr for your team may well have been lower despite having the higher ranked player.
(Also, I assume you're talking about current ranks and corresponding current mmrs. The system doesn't care what they used to be in terms of mmr and LP calculations, so ex diamonds and ex plats who currently have gold mmr and gold ranks are exactly the same as people who've never climbed from gold and have gold mmr/rank.)
edit: Also assuming solo/duo queue. Things are really cray over in flex, as in many cases their solo rank has nothing to do with their flex rank.