PNG is lossless but do not misunderstand that DDS is lossless. While DDS is just a container format, usually it is associated with S3 compression which is lossy, so anyone telling you to use DDS is asking you to use lossy compression.
To expand on why you want to use either lossless formats or lossy S3, but not other lossy formats:
While a jpg file is smaller on disk, when sent to the graphics card it is expanded into a bitmap, so you lose the primary benefits of the compression. You get a worse looking image that takes up the same amount of space in VRAM.
A lossless format is better, because you still get smaller file sizes (but again it is expanded to a regular uncompressed bitmap in VRAM), but no loss in quality.
S3 is special because even though it is a lossy format, it is supported by hardware and doesn't have to be expanded into a bitmap. So you get a huge size reduction compared to lossless compression, and you get to carry these size reductions into VRAM. Textures make up quite a large portion of VRAM budgets, so being able to cut your texure memory usage by as much as 75% with almost imperceptible loss in quality is quite nice. You also get better performance because the texture cache can hold more of a texture, and the memory bus has to work a lot less to transfer textures to the graphics card.
No games use .X as a native format
I was quite surprised a few months ago when I was randomly browsing through a medium-budget game's directory and discovered a bunch of loose .X files. I tried to load them in some of my own code, and sure enough, they were models
I just wish I remembered what game it was...