A wesbite designed for both smartphones and bigger screens is much better than a website designed just for larger screens but it still can't do everything you can do with an app.
So should you develop for Android or iOS on an iPhone? A good approach is to start with one and then develop for the other. There is no magical one click solution to convert from one platform to the other so the best approach is to work out all the niggles with one first over a period of months.
We recommend Android as they have over four times the market share.
So after we've sorted out all the niggles for you then you're you ready to get it working on one of these, an iPhone.
If you decide to. It's not compulsory and as we said Android have got the vast majority of the market share.
If you want to look into it you'll need to get some quotes from people who can develop your app for iPhones.
That should be easy just get them to download your Android app, have a good look, and give you a quote.
You can then decide whether it makes financial sense.