More storage space is the only difference. The "performance" will be the same.
As to whether it would "be worth it", ...
1) Typically, you will want to buy as much storage as you can afford (apps, files, music, etc will only get larger and larger over time). (Even at the $100 premium that Apple charges for the space, it is typically worth it for most users.)
2) How do you/they plan to use the device? Will lots of music, videos, apps, etc be stored on the device? "How much" space is needed is really an individual question. Some people will argue that you don't need a lot of space on the device because "everything can be stored on the cloud". The fallacy in this argument (in my opinion) is that with the advent of carriers going away from unlimited data plans, the "advantage" of being able to put everything in the "cloud" needs to be weighed against how much data all that transferring will use. Again, this is a personal decision based on the usage by the user.
What size iPhone 4s are they using now? How much space is being used? Do you anticipate a change in the usage? These are the questions to ask the user.
You answered your own question. The more space you have the more space for Music (if not over icloud) photos and Apps which if you are a light user the 16 GB should be OK.
You must also remember updates to the device, updates to apps, saved files from the owner all will add up.
Good Luck on your choice.
thanks to both.
college student using phone. Takes a lot of pics and mostly txting and a lot of facetime with BF and family that is 3000 miles away. Not so much music as she has 32gb touch.
I'm taking away a 16gb will probably get he by.