The EU Parliament is not democratically elected because votes from member states have a different weight. The election is free but not fair. It's also one of the few parliaments that can't propose laws on their own but can only veto laws proposed by the EU Commission.
The powerful EU Commission being appointed by governments (and again only approved by the Parliament) is a form of executive federalism. This makes the chain of legitimacy longer and longer which is hardly positive for democracy.
Small states are usually given more weight in parliament. This is commonly considered more democratic.
The commission is elected by the parliament. This is democratic.
Would it be an improvement if parliament could propose laws and commission members. Maybe. But saying that this makes the EU undemocratic is unreasonable.
in most contries votes have different weights. look at the US, or other western countries where minorities for example are boosted to be represented in the parliament. judging by this no country is democratic.
In the US, votes in the congress, senate and president have exactly equal weights between states? Not an expert but I suspect we're in the kettle-pot area here. Not even getting into abysmal voting procedure/implementation which would be inconceivable in the EU.
The powerful EU Commission being appointed by governments (and again only approved by the Parliament) is a form of executive federalism. This makes the chain of legitimacy longer and longer which is hardly positive for democracy.