In my experience, PNG isn't a 'great' format to use, because of its compression, which can sometimes bring some oddities to the image itself. Basically, they are generally lower quality than .dds or .tga.
While .dds and .tga are generally much higher file size, they are also (generally speaking) better quality and with some engines, preffered.
I myself work with .jpg when I want to quickly view something (as it shows on thumbnails and is usually quicker to save as), but for final textures, I use .tga.
Like Scene Commander said, it is more of a preference thing, an image is an image.
On the note of using converters -
Generally, it's better to save directly to your format (where possible) rather than use a converter.