Both are good as both have 17 titles.
This depends on your criteria but there is a strong case for either side. They both have 17 league titles since the inception of the current league format (in 1959), but overall Fenerbahçe holds 26 national titles to Galatasaray's 18. However, Galatasaray holds more cup titles and has a UEFA Cup to their name as well.
galatasaray besiktas fenerbahce arsenal man u man city
Fenerbahce was originally founded in 1899 making it the oldest soccer club followed by Besiktas in 1903 and Galatasaray in 1905.
Galatasaray (Ali Sami Yen Sport Centre) TT Arena stadium, Istanbul Turkey by Galatasaray fans. 131.76 decibels. The game was played against Fenerbahce where they lost 1-2. 18 March 2011. Guiness officials were present.
Galatasaray Athletics was created in 1868.
Galatasaray Community was created in 1988.
Galatasaray University was created in 1481.
Galatasaray TV was created in 2006.
Galatasaray Judo was created in 1984.
Galatasaray Swimming was created in 1873.
Galatasaray Rowing was created in 1873.
Galatasaray - magazine - was created in 2002.