Upgrading from Galaxy S2... thoughts?

I've had a Samsung Galaxy S2 for a few years and now I'm looking for an upgrade. Reasons:

  • 4G: S2 lacks LTE support
  • Usability: S2 is a bit slow running some apps (e.g. satnav apps) and grinds to halt in heavy use (phone encryption enabled, animated background, satnav running, soundcloud streaming music to bluetooth)

I'm after a phone which has:

  • LTE supported
  • a removable battery
  • a 3.5" screen or larger
  • a 480x800 pixels screen or higher
  • a 125x65x12mm body or smaller (i.e. no larger than the S2)
  • reasonable support for custom roms
  • removable storage
  • the ability to cope with heavy use

I know 'heavy use' can mean a lot of things (for example do I really need an animated background?) so I appreciate there will be some compromise. But it would be nice for the phone to pack a punch.

My searchings haven't come up with much. The Xperia Z1 and Z3 Compacts come close (slightly tall and no removable battery). The Galaxy S4 mini is a good contender but its CPU isn't much better than that of the S2.

So questions:

  • Users of Xperia Z1 and Z3 Compacts - what are your battery lives like?
  • User of the Galaxy S4 mini - how powerful is the phone?
  • Any other suggestions?

any of the galaxy phones before the galaxy s 6 i would recommend; i dont recommend the 6 as its almost an iphone clone with android.
i would also be comfortably recommending the HTC one (any version) but those are kinda expensive but about the size your looking for
the oneplusone is also an option but is a touch bigger that what you looking for
now if your looking for a lower dollar phone then i think the new asus zenfone 2 would fit just fine

For closure. I got the S4 mini and I'm very happy :)

I went from the s3 to the note 4 love having a larger phone. The only down side I had with it was having to root right outta the box to get that facebook and crap off of it. I'm sure other new models do the same thing though as well now. Really any of the new (flag ship) phones now days are all the same performance wise.....are you doing contract or buying the phone out right? cause price range is the best way to figure ones options.