Why Convert?
If you are working in PSE or PS with a .jpg file every time you save the file as a .jpg you will re-compress the image. and loose detail and Jpg artifacts will appear in the image.
Batching in PSE
Menu File > Process Multiple Files
You get this requester in PSE 8

You select the source and destination for the files
Set up your renaming scheme
Choose file type…
you can also do some “quick” processing, water mark the images or add a caption.
Batching in PS
Photoshop doesn’t have a “batch” Dialogue Box/Wizard
1. Use the Bridge to send a batch of .jpg files to Camera Raw
Highlight the images
right click (pc)
Click mouse + Control Key (Mac)
Choose “Open in Camera Raw”

2. in Camera Raw Top left choose Select All (1) then Save Images(2)

You’ll get a robust conversion dialogue box that will allow destination, renaming and several file types…

What’s neat about this process is 1. It’s really fast and 2. you can start multiple conversion sets one right after the other…
Gota a question ‘holler