My wife uses an iPhone 4 and seems to like it. What do newer iPhones do that would make worth upgrading?
I am going to compare to my current phone (iPhone X) and the phone I am getting next week (iPhone XS Max)
Larger screen - iPhone 4 has a 3.5" screen. iPhone X is 5.8 in. iPhone XS Max is 6.5 in. I have an iPad Pro and I am going to sell it because I've determined that I no longer need both an iPad and an iPhone.
Much longer battery life - iPhone 4 (new) is 14 hours. iPhone X is 21 hour. iPhone XS Max is an hour and a half longer. Also with an iPhone 4 I would expect the health of the battery is probably pretty degraded.
Screen resolution - iPhone 4 is 960 x 640. iPhone X and XS Max are 2436 x 1125
Display type - iPhone 4 is LCD. X and XS Max are OLED
Waterproof - iPhone 4 is not. XS Max is (to a point).
NFC support - no on iPhone 4 - Yes on iPhone X and XS Max
Camera -- much much better on iPhone X and XS Max. Rear camera and
front camera resolution on iPhone 4 is 5 MP. On iPhone X it is 12 and 7.
SIM card - Note that new iPhone XS and XS Max will be able to have 2 SIM cards. I don't need it but some people do.
Broadband - iPhone 4 is 3G and iPhone X and XS Max are 4G. This is a big deal for anyone who uses there phone for things other than talking on the phone. Interestingly, I just found out that Verizon won't let you activate a new phone on their network that is not 4G. We had a small flip phone we had taken off the network a few months ago that was 3G. We wanted to put it back on. We couldn't because it is not 4G. The point is that if you were to change cell carriers you might not be able to activate an iPhone 4 on some networks.
Apps - Lots and lots of apps won't work on an iPhone 4. You can't upgrade to iOS 12. There lots of features that you can't get on an iPhone 4. You can't get Face ID, etc.
Now - if you don't care about any of the smartphone features of your phone and just want something to be a phone then there may not be a reason to upgrade. Wait until the battery dies and then replace it, maybe with an Android phone. There is absolutely no reason to pay the cost of an iPhone if you aren't going to use the smartphone features of an iPhone.