The EU could absolutely find ways to hurt the US economy just as much as vice versa. It doesn't have to use the same tools as the US. Just ban major US companies from doing business in the EU. Impose massive fines. Get creative.
The EU economy is on par with the US economy. The EU has plenty of ability to hurt the US economy.
The reason this doesn't happen is because the EU isn't a country. It doesn't have a unified central government. It's 27 different sovereign states, each with their own completely different foreign policy. The type of policy I'm describing requires a unified political leadership willing to play for high stakes.
This is why China has been so much more effective than the EU in the trade war with the US. It's not that China theoretically has better cards to play. It just has a central government.
EU economy is not on par with the US economy. This is a dangerously old belief. That was maybe true in 2000 but not in 2026. EU GDP per capita is ~$48k and US GDP per capita is ~$94k. US economy is nearly twice as big. Quarter of a century of higher growth will do that.
EU does run a trade surplus with the USA. In a big fight the USA would, strictly speaking, have to replace more stuff than the EU would. However that ignores the makeup of the things being traded. EU exports to the US is dominated by pharma products that the US could make generics of, misc machinery that can often be replaced by Chinese competitors now, and luxury goods the US doesn't strictly need. US exports to EU are critical for the functioning of the economy (assuming you count tech services as exports).
It would be catastrophic for the world if there was a serious trade war between US and EU but if it involved major disruptions to tech services the EU would fold within days. There are no home grown replacements for most US software and no ability to make them anytime soon (especially as any broad spectrum sanctions would include frontier AI models).