The entry fees for chess tournaments in my country are from 100-300 USD, so it does involve losing money - although the cash prizes and stakes in poker are much greater.
Poker is psychologically greater because there is bluffing involved. In chess, bluffing is much more difficult, especially in the long time controls that give out big prizes.
As for online chess or online poker, it's no big deal, just learn from your mistakes.
Anyone who cries or feels depressed for a long period of time when losing a chess game or poker game, especially online, should learn to be more mentally stable or stop playing.
We know that suffering a loss can be hard in chess. Especially if you fought hard and was close to a draw or maybe to a victory. But how does it compare to the impact that a loss in poker game is having on a player?
I would say that poker is more difficult psychologically than chess, since a loss in poker involves losing money. In chess it doesn't.
However there are players who cry and feel depressed or infuriated if they lose...