[Twig] Compare date with a specific one and DateTime to stri

[Priestess]

Hello everyone! I have two questions:

1) How can I compare two dates in Twig when the first one comes from the dababase and the second is clear - 2012-12-31? I tried with

{% if dom.dueDate|date('Y-m-d') > 2012-12-31 %} but I don't get the result I want.

2) I have a DateTime field but I couldn't find a filter for DateTime in Twig and when I use |date('Y-m-d') it prints only the date without the hour

I would be really happy and grateful if someone helps me to solve the problems!