To best answer this question, I feel like a direct comparison between these two events is necessary.
OLD IMPERIALISM (c. 1450 - 1750)
Old Imperialism is a term used to describe the imperialistic events of the Europeans towards the indigenous tribes of America. It all started when Christopher Columbus sailed across the waters to America.
The motives for this wave of imperialism could be summed up in three words: gold, God, and glory. You may of heard these before.
Gold. Europeans wanted a lot of gold since their supply back home was running out. Constant wars with neighboring countries and frequent peasant revolts didn't come cheap.
God. Europe also wanted to spread the word of God. Lots of missionaries and activists traveled about, jumping at every opportunity to convert people.
Glory. Europe's heavy view of ethnocentrism acted as a catalyst to conquering lesser advanced civilizations. They thrived to make a mark everywhere they go, and wanted it to stay.
And just a side note, gold was an active reason, while God and glory were passive.
When Europeans encountered the indigenous tribes for the first time, it did not end well. They killed thousands, decimated their homes, and took their lands.
They forcefully converted almost the entire population to Christianity through ways like Residential schools. They also enslaved many people.
NEW IMPERIALISM (c. 1881 - 1914)
Before I get started, I would like to point out that the information presented in the following lines are specifically from African imperialism. I'm not exactly an expert as to what happened to other places during the era of New Imperialism, but the ideology should be somewhat similar.
This time around, the motives were way better. Of course, they weren't great, but at least they were better than the old views of gold, God, and glory - kill everyone, take their land, and here, have my smallpox. Europeans actually wanted to help the people of Africa. This was because of their new views like the White Man's Burden. But of course, they were also still greedy for territory.
European colonialism brought many forms of sports to Africa, connecting it to the rest of the world like the African Cup of Nations (soccer tournament). The previous form of government, like the Isalmic rule, was also way worse to the society than the European rule. Europe even abolished some forms of slavery! European imperialism also brought over education, and the basis of which is still being used today. Europe brought over new cures and treatments for diseases, helping millions of people in Africa to live cleaner lives.
There! Hope this helps.