I would say that either a synth or an arranger can meet those specifications, depending on the unit. Plenty of synths offer split and layering of the sounds -- you would just have to make sure the synth you purchase has those features. And both synths and arrangers can have very authentic sounds, with, in general, more expensive units having better sound circuitry (though, these days, even lower-cost units can sound very good).
What really differentiates the two is the amount of automatic background style/accompaniment that is available, as well as how deeply the sound can be edited.
Arrangers, of course, have more comprehensive background styles and accompaniments -- that is really the defining purpose of an arranger. Synths can have some backgrounds built in, but it is often limited to drum patterns and arpeggios.
Synths can get down to the very basic essences of the sound -- such as the basic waveforms -- then let you take multiple steps to modify, shape, and customize the sound, such as using filters to alter the sound, envelope generators to change aspects of the sound over time (from the time you hit the key to after you let go of it), and low frequency oscillators to add modulation such as vibrato, tremolo, wah-wah, and other effects. Many higher-end arrangers provide at least some degree of this type of sound shaping, but usually not to the extent of a dedicated synth.
If automatic background styles are very important to you, I'd go with an arranger. But if creating your own unique sounds is more important, then I'd go with a synth. With the synth, however, if you at least want drum backgrounds, make sure that this capability is available, and check to what extent it is available, such as having the ability to provide intros, fills, and endings. Getting a separate dedicated drum machine is also a possibility.
With built-in speakers, you are much more likely to find that on an arranger than a synth, but you said that is not a deal-breaker.
What I have done is select both options! I have a PSR-E433 as my main keyboard. I generally do not use full auto-accompaniment styles, but I definitely do use the styles for drum backing, and the intros, fill-ins, and endings are important to me, even just for the drum backgrounds. But to get more custom sounds, special sounds, and sound effects that simply cannot be done on the E433, I have also added a Roland Gaia SH-01 synth to my set-up. This is a small 3-octave synth with great capabilities that makes a great companion to my E433, and also gives me more orchestration options by being able to quickly change the sound that I am playing during a song by simply jumping from one keyboard to another. Of course, adding a second keyboard to your set-up would affect the overall portability of your system, especially if you need to add outboard speakers, so that is also something to consider.