Some quick thoughts....
I'm not very familiar with Aristippus and his ideas. But for Epicurus it was very important to have a correct view of the gods and death, meaning a correct world view, as a central component of a life of pleasure. So I'm curious as to the world view of Aristippus was.
In another thread we've been discussing pleasure and some of the PDs. One approach to comparing the two philosophies would be to compare "a constant round of active pleasures" to pleasure as described in PD03, PD09 and PD10. For instance PD10 could be read as a direct Epicurean response to Aristippus, although I don't know if that's historically accurate.
QuotePD10 If the things that produce the delights of those who are decadent washed away the mind's fears about astronomical phenomena and death and suffering, and furthermore if they taught us the limits of our pains and desires, then we would have no complaints against them, since they would be filled with every joy and would contain not a single pain or distress (and that's what is bad).
Looking at PD03 is tricky as it's usually mentioned as a rebuttal to Plato. But what if you look at it as a recipe for the best life, from which you can and should draw your own conclusions? If you are striving for the greatest pleasure, how could you go about it? People immediately jump to "Remove all pain! Remove all pain!" But is that really what he's saying? True, if you've reached the limit of pleasure then you won't have feelings of pain. So how do you do that? If you have pleasure in your stomach for a moment then there's no pain in your stomach for that moment. If you have peace of mind for a moment then there's no pain in your mind for that moment. Knowing this, you can strategize how to achieve the longest lasting, most complete and most sustainable experience of pleasure.
QuotePD03 The limit of enjoyment is the removal of all pains. Wherever and for however long pleasure is present, there is neither bodily pain nor mental distress.