The Reds may have a bigger trophy cabinet and worldwide profile, but the Toffees have finished above them in the league in the last two seasons and sit just a point behind them in fifth in this season's table.
Manager Roberto Martinez's arrival in the summer has brought a more positive outlook at Goodison Park and Everton head to Anfield on Tuesday more confident than previous years that they can secure their first league victory there this century.
"It is hard to live in their shadow when we've finished above them the last two seasons," said Osman.
"We hadn't won at Manchester United for 21 years or so and we went there and did that (last month) on our first attempt under the new manager.
"It is probably more of a hurdle on paper than it is within the dressing room or our minds because we are positive and under the new manager we are confident we can go there and win.
"I am sure we will attack them as the manager has one way of playing and he won't want to change that just because we're going to Anfield.
"I am sure we will go there and play the same positive football we have been playing all season and probably expect to come away winning the game."
Their encounter in November at Goodison was a thrilling affair, one of the most open derbies in years, and finished 3-3 after Liverpool substitute Daniel Sturridge scored an 89th-minute equaliser.
It makes a Merseyside derby even more enjoyable, according to Osman.
"We are certainly playing the football we seem to enjoy at the minute," he added.
"It is great to be involved in and it showed in the last derby game what it is like when two teams go toe-to-toe.
"We say it every year how much of a special occasion the derby is and we look forward to it, but this year we are both challenging towards the top end of the league and there is more than pride at stake this time.
"It (the November derby) was a special match which had everything. The only thing it didn't have was a winner on the day so I am sure both teams hope it is just as entertaining and we hope we come out on top."