I have travelled both with a pump and on MDI, and personally I find it easier to travel with a pump for several reasons. I can adjust or even suspend the basal to accommodate varying or unpredictable levels of activity. It’s a breeze dealing with time-zone changes compared with half-doses of long-acting that always seem to send your sugars out of whack for a day or so. I find if I’m eating in a public space (Southeast Asian street food – yum!) bolusing with a pump is easier and more discreet than injecting with a pen (others may think the reverse – it’s a very individual thing). And I’ve always travelled light, so the “bulk” of pump supplies has never been a problem, and supplies are very light to begin with.
Pump or injections, a challenge at this time of year will be keeping your insulin in a safe temperature range. Many people swear by Frio bags (search on this site).