You basically have two options. First, keep everything in the flat and do a fast move in one day. That is cheapest, but only if your handover dates line up and your landlord is flexible. Mine was not. I had a 5 day gap and boxes everywhere, plus building move-in slots, lift booking, all the usual Dubai fun.
Second option is storage for a couple of weeks. I ended up using a short-term unit after comparing a few places through Storage Companies Dubai. Not glamorous, but it solved the real problem, which was time. I could deep clean the old place, get maintenance done, and move into the new flat without rushing.
A few practical things:
* Take photos of furniture before movers dismantle it
* Keep one suitcase out with clothes, chargers, docs, meds
* Ask the building about lift timing before booking movers
* Do not store passports or jewelry in random moving boxes
For area tips and the usual Dubai living stuff, I still check Time Out Dubai now and then, especially if I am trying to get a feel for a neighborhood.
My verdict: if there is even a small gap between flats, pay for storage. In Dubai, paying a bit for less stress is usually worth it.