The organizational strength the LDS church has is allowing it to be a strong and powerful influence for good in the world.  At 15 million members, the church is now getting large enough to be a presence in the world and contribute in the national and global community on important issues.  The church doesn’t publish financial figures, but as of this 2015 writing it’s estimated the church takes in $6B in revenues per year from members in the form of tithing and offerings and has financial assets in the $50B range.  Some church critics think this is a bad thing, but I believe it’s a tremendous asset for the church in its efforts to do good in the world.

A complaint of the church is that things out of Salt Lake sometimes feel corporatized.  The church’s business arm, understandably created to protect the financial viability of the church and maximize the good the church can do given the donations it receives, has grown into a corporate behemoth.
This seems to contradict the Jesus of the New Testament and even the small church Joseph Smith started.
But the LDS church in the 21st century is not a small, local religion. Jesus in his earthly ministry was not leading an organization of 15 million members. Joseph was not managing a global church with 30,000 units in 160 countries and 180 languages. It’s a difficult job for the brethren to create the same kind of focus on the individual the early Christian church in the time of Christ and the early restored church in 1830 had, while keeping a level of consistency and unity across the modern LDS church.
It’s our strong, central leadership precisely that has enabled the church to grow and consistently maintain the good experience that members have across the globe.  Many of the things we love about the LDS church are only possible due to that organizational strength.
The church has over 80,000 full time missionaries.  Some of those are service missionaries, but all of them are required to do at least some non-proselyting service each week.  The church responds quickly to aid in natural disasters.

Some believe the church chose the wrong battle to fight Prop 8, but the church definitely learned a valuable lesson in the process.  The church has a lot of power.  When and where it chooses to use its resources to affect change will be interesting in the future.
Another benefit of the size of the church is the networking potential for members.  Pick a city in the world and likely there is an LDS ward or branch there and a visit there would find instant friends with common interests.
The strong, central management the church has can allow it to change quickly and maintain doctrinal and teaching purity.  The church has seemed to move slow to respond on certain issues, for example allowing black members to receive the priesthood.  Church leadership usually take a literal view where past teachings of prophets are critically important, which makes change awkward, as many times it calls into question the rightness of a past teaching.  If church leadership could take on more of a symbolic/sacramental view, church leaders might be more comfortable embracing change and leading change in society.
Membership size is not proof or disproof of truthfulness, but a large church can help attract and retain members.  Church growth has slowed the last 20 years, but we are still growing faster than most religions.  Over time, the power the church has in the world to relieve suffering and bring people to God will increase.  If we believe in this church, we should continue to work to help it grow.