Back to OP's original question, Yes the S4 will be a pretty good improvement over the EP630. Everything will be stronger on the S4, and you will do best letting them play connected to a repeating CD for about 2 whole days (40-50 hrs.) to let the drivers settle down a bit. The S4 can seem harsh straight out of the box -- you can certainly listen to them for a bit to see how you like them, but let them burn in before you make your critical judgement on it. Even then, you might still want to EQ down the bass just a tad, unless you like slightly overwhelming bass response.
Also, the Clip + S4 combo will be fine, and you won't need an amp to drive the S4's sufficiently. Having said that, when you can afford even the little Fiio E5 for $25, it is a good improvement -- it will sharpen the sound going to the S4.
Also, the Clip + S4 combo will be fine, and you won't need an amp to drive the S4's sufficiently. Having said that, when you can afford even the little Fiio E5 for $25, it is a good improvement -- it will sharpen the sound going to the S4.