The Gunners have moved five points clear at the top of the table on the back of some sparkling football which has won them plenty of headlines and admirers.
But Welsh wizard Giggs believes United's steel and their ability to win ugly as well can ultimately see them retain the Premier League title.
Giggs told Inside United: "I did notice the praise Arsenal were getting earlier in the season but it didn't really bother me.
"Arsenal were playing good football, but we felt we were as well.
"It's always been the United way to try to win with good football but our ability to win ugly as well has been a trademark of the last 15 years or so."
While Arsenal have lost only one league game this season, United have now lost four following their derby-day defeat to Manchester City at Old Trafford. But many believe there is still a brittleness in Arsenal which could show itself in the final run-in.
Giggs says the big test comes when teams have you under the cosh or set themselves out to gain a draw.
Giggs said: "In the majority of games, we're going to try to play attractive football and score lots of goals but we also need the added steel for games like the ones at Liverpool this season and last.
"We did not play particularly well in the last two games at Anfield but still managed to sneak a win. They are the kind of results that really do win leagues, not the big wins like 6-0 against Newcastle.
"You find that every team you come up against in the Premier League is playing for something, whether it's battling to stay up, going for a place in Europe or trying to win a title.
"Many of those clubs would consider a point against United to be a good result, so you're coming up against sides that maybe don't intend to win.
"They just want to defend and get men behind the ball and that's what we'll have to try to overcome - teams that are trying to stifle our play."