ばいい・といい: the difference
ばいいN3
Meaning
Can, Should, It'd be good if
Past papers
Tested 2 times in past papers
Example
運動をすればいいだろう。
It would probably be good if you exercised.
といいN4
Meaning
I hope, I wish, You should, It would be good
Past papers
Tested once in past papers
Example
試合で勝つといいですね。
I hope that you can win the game.
How to tell them apart
Add 「のに」 (「～ばいいのに」) and it means 'I wish you would...', with regret or mild blame that it wasn't done.
「～たらいい」 is more casual: 「どうしたらいい？」. 「～といい」 is mostly a hope: 「明日晴れるといいね」 (I hope it's sunny tomorrow).
「～ほうがいい」 is firmer advice after comparing options and can sound rude to elders; 「～ばいい」 is softer.