You got a 5DmkIII and you use Picasa to convert your RAW?
That's really something... get at least LR, or better DxO and Photoshop: you'll finally really take advantage of your amazing camera.
Will this DxO and Photoshop offer an advantage over LR, or even DPP as a RAW converter?
Photoshop uses the same conversion engine as lightroom, but has a lot of editing features that can be used. It also takes a lot of practice to understand them and use them.
DXO tends to produce very good and sharp images upon conversion, but is also slow and attaches sidecar files with the conversion formula that must be kept in the same folder as the image. LR keeps the conversion and edit info in a database, but has a option for sidecar files, or for writing the info into a DNG file.
It really boils down more to personal preference, each has its pro's and cons. With LR dropping their price by such a large amount, Lightroom is going to be very popular.
Another popular low cost editing tool is ACDSEE PRO.(The non pro version does not edit in RAW) I used it for several years with jpeg images, but when I switched to using RAW, I went to lightroom. RAW files is not as user friendly as Lightroom.