One of the biggest differences I can think of is spices. Not that an English nobleman wouldn't have ever had any, but almost any spice coming to England from Asia would have had to come through Constantinople - a Byzantine would have almost certainly seen more variety and maybe even quantity in spice than anyone in England, especially if he's frequenting the ostentatious and glamorous banquets of Manuel I (and doubly so if the emperor is trying to impress western guests). The Oxford Dictionary of Byzantium says the Byzantines even had caviar, though I've never encountered a description of it myself. The Byzantines were well-known for a relatively refined dining culture throughout the Middle Ages - it was a Byzantine woman who re-introduced the fork to the court of the Holy Roman Emperor - so I imagine an English noble in Constantinople would be (at least relatively) impressed by the cuisine. This thread gives a little more background on Byzantine cuisine, and helpfully links to a great deal of secondary literature.

The other most salient difference I can think of is, of course, eunuchs - essentially totally absent from the west, still relatively ubiquitous in Byzantium, even at this late period - but they're definitely not climate-related and although there's some economic factors in determining their use I'm not really an economic historian, so I'm not sure how relevant they'd be to your interests. Eunuchs are extremely expensive - to obtain and to employ; monetarily, but also in terms of human life - but they seem to have not been used in the west mostly for cultural reasons rather than economic ones.