There's two central drawbacks to moving past Direct3D 9.0c.
- You have a slightly higher minimum requirement when using FEATURE_LEVEL_9_1 in a Direct3D version that has lower feature levels. Some of the lowest end cards that can work in Direct3D9 are not quite able to satisfy the low requirements of level 9_1.
- The minimum required operating system for 10 and up is Vista, and for 11 you need Vista SP2 (with platform pack). If the XP market is important to you, this may be a showstopper.
You also have more and more trouble using the DXSDK with Visual Studio versions 2012 and 2013, as those use the new Windows Kits which have conflicting headers present and require much care in picking up the right definitions and libraries.
The benefits are many, among others continued support of the SDKs involved. When the DirectX SDK was folded into the Windows Kits, you lost both D3DX and Direct3D 9. As the SDK was discontinued, there's no fixes for the bugs existing back in June 2010, and which still exist to this day. As modern DirectX is part of the platform, it's much more serviced and integrated into the IDE, and deployment is somewhat easier.
There's a bit more overhead in the amount of work you will need to do to get something equivalent running in D3D11 compared to fixed function pipeline D3D9, but it's not necessarily consuming more resources as alluded by others here.
I would go so far to suggest that a more modern DirectX version is better for doing 2D graphics, as you're less tied to the 3D-oriented semantics that Direct3D 9 used to have, and can make your shaders and data bindings in a much more true-to-the-data way.
If you're starting from scratch, I would not recommend ever starting with an essentially dying legacy technology. Go for D3D11 or modern OpenGL.