Picasa Web Albums has a functionality to transfer photos from your one account to another account. But, because of some problems, it recommends that not to use it. If you use it, may be your both accounts get stuck in a read-only state.
When you upload photos to Picasa Web Albums, the copies of photos will upload to the Google servers and the high resolution originals remain on your computer's hard disk. So, if you want to upload photos to your new account, then instead of downloading them and again uploading them to a new Picasa Web Albums account, you can simply upload the originals to the new account.
Picasa has a "Batch upload" feature which allows you to upload photos in a batch. If you do not know how to batch upload folders to Picasa, then you can follow the link provided here.
If you want to use the different Picasa Web Albums account, then you need to click "Sign out" link located at the Picasa's upper right corner. Picasa will prompt for a Web Albums logon name and password the next time you do an upload.