Marilyn, TIFF files are just like PSD files - they are all in layers. There would be no disadvantage to converting but it would be time consuming if you have a lot of templates. Also Marilyn if you are creating a layout in your PSE and you go to "save as" you should see TIFF as a format that you can save your layout in.
From what I have found on the internet: TIFF was the format for programs that could not use PSD which is a product of Adobe.
(Someone else with lots of computer knowledge may come along and explain fully the differences)
I just looked in my folder of zipped downloads for a template I have downloaded this month.
The PSD file size is.... 83.9 mb
The TIFF file size is.... 68.1 mb
This is why some people who want to save room on their computers only keep the TIFF files which is what I have started to do.
As you create your layouts you could save in TIFF format to save space on your computer if you are going to keep the layered file. ( this is something I should start to think about as I have so many PSD files from past layouts that I really do not need to keep. Each year I move my year of PSD layouts onto a EHD. Maybe I need to decide if I ever really need to go back and redo the layout as it all is just taking up lots of space on my EHDs).