I like gsmarena.com for looking up random phone specs and doing comparisons although I couldn't find a "search by size" feature. Your SIII Mini has a 4.0" display and was released in late 2012. It's only 4.8" x 2.5", so that's pretty small by today's standards. I used a first gen Moto X for years and had great luck with that phone. The second gen Moto X was released in 2014 and has a 5.2" screen, but it's 5.5" x 2.8" so definitely larger than your current phone.
As far as new features go, I really like the rear mounted finger print sensor on my Pixel 2 for unlocking my phone. It just falls to hand when you grab your phone out of your pocket. The Nexus 5X has this feature, but it is not a current model and it measures 5.8" x 2.8", so even larger than the Moto X Gen 2. I sympathize with your desire to have a phone that fits in your pocket, but I think you're up against a trend towards bigger phones, or screens. I confess that I think the iPhone X is about perfect in that respect. Unfortunately it costs upwards of $1,000 and face id is not really ready for prime time.