If being able to use a phone with one hand is important to you, then don't upgrade to a bigger screen. I actually downgraded in size to a 4.5 inch screen and I'm a lot happier. I can make phone calls with one hand, text with one hand, scroll web pages with one hand, launch all my apps with one hand, etc.
Bigger screens are nicer for longer viewing sessions, but I find that during the day I only quickly glance at my phone, then turn it off again. I'm only using my phone to read texts, emails, or check FB quickly - none of which take longer than a minute.
If I want a bigger screen for longer sessions like web browsing or watching a video, that's what my tablet is for.