This is a question that concerns many pastors and church boards. My answer is very simple: You don't compete! You don't need to. Before I share some practical suggestions let's look at some realities of how and where people give.
Many pastors teach storehouse tithing or giving. In other words, the tithe belongs to the local church (see Malachi 3 as a common text) and anything over a tithe is fair game for any ministry. The problem with this is twofold. First it assumes that the tithe is the standard in the New Testament. I would suggest it is not. The New Testament standard is generosity in our giving to God's work (2 Corinthians 8-9, 1 Timothy 6:17-19). It is a lifestyle of generosity in all respects including giving.
In addition, and many pastors don't get this, the most wealthy congregants are often not going to give ten percent of their giving to the local church because it would overwhelm the budget and creates dependencies on that donor. I suspect that on the issue of storehouse giving, pastors preach it and congregants largely ignore it.
I do, however have four suggestions for pastors and church leaders. The first is to communicate the central place that the local church plays in God's economy and plan for the world. Every local church is a kingdom outpost from which God intends to reach the world. God specifically chose and designed the local church as his instrument to reach the world rather than para church ministries which should serve the local church in its mission. The better my understanding of the central role of the church, the more likely I am to be generous in my giving to it.
Second, talk vision rather than financial need. Giving flows toward vision! And here is a critical point. If your congregation has significant vision for what they believe God wants to do in and through them and if they are seeing God work on a regular basis, giving will come. Not because you have a mortgage or salaries to pay but because you have a vision for your congregation, community and world. Giving flows toward vision!
Many churches suffer from chronic monetary shortages not because the resources are not there but because the vision is not there. And, I fully believe that God always provides for what He has called us to do. When the funds don't come in it is usually because our vision is too small or we are doing something God has not called us to do.
The last point leads me to a caution. If the vision we are raising money for is the vision of an individual such as the pastor or influential leader rather than the vision of the leaders and congregation it will often suffer. The church is not a vehicle for us to see our individual dreams realized but to see a corporate mission accomplished. When giving goes down be aware that it may mean that people are voting with their pocket book and have not bought into a shared vision. Often when giving goes down we put additional pressure on people to give when in reality we ought to work harder on a shared vision.
Putting pressure on people to give often has the opposite effect. We don't like to feel manipulated or pushed. Encouragement is great, pressure is counter productive.
Third, thank those whose spiritual gift is giving. Do it appropriately but thank them. Other ministries do. And we thank those who use other gifts in the body, why not this one? Let them know how their generosity is impacting the mission and vision of the church for the cause of Jesus.
Finally, here is something to consider. We are told by Paul to be content with what God gives us. Can that also apply to congregations? Do we believe that He provides us with what is necessary to do what He as actually called us to do? Can we live within our means as a congregation as we teach families and individuals to do? Something to think about.