Barca slightly edged them out for that period, but Madrid are still the biggest and most successful club in the history of football.
I say slightly because in the grand view of things domestic titles are just not as important as UCL wins. Think about AC Milan and Juventus. Globally, Milan are way more famous because they did well in Europe even though Juve are way ahead of them domestically.
Premier League - None
La Liga - None
Ligue 1 - None
Bundesliga - Dortmund (have a soft spot for their commitment to youth development and exciting style of play)
Serie A - Inter (my team)