When you say "political group," I assume you mean something like a political party. Interest groups and political parties are effective at different things.
Political parties are effective at creating large coalitions of people and organizing them in government. They bring together people with many different interests and emphasize what they have in common. They then use support from this group to get power in the government.
Interest groups are effective at pushing for what they want on specific issues. They do not try to make coalitions or run governments. Instead, they focus only on what they care about and they pressure people in government to support them.
Both of these kinds of groups are effective, but they are effective in different ways.