Having gone on international trips with my baby with both a stroller and a carrier, I’d say there really is no clear choice between one or the other. It really depends on several factors. First would be the comfort of your baby and his/her personal preference between the two modes of transport. When my baby was really just an infant, she didn’t mind being in a stroller. Now that she’s entering her toddler stage, putting her in one is really quiet a challenge. These days, she’s less resistant to being carried with a cloth carrier (surprisingly). If you’re baby isn’t so fussy about either methods, next thing to consider would be accessibility of the location. Strollers are extremely difficult to manage without lifts/elevators. You will have to carry your baby and the stroller up and down several flights of stairs of your destination is not baby-friendly.
If you intend to go to parks and take a lot of walking trips, then a stroller would definitely be the way to go. However, if you are taking public transport (like buses, subways or metro trains), check first if these are stroller-friendly. In most cases, they are not.
Carriers are great when moving from gate-to-gate in airports where you have connecting flights. When travelling with a baby, you will most likely gate-check your stroller. In this case, there will be a time when you will have no assistance for carrying your crying/sleeping child as you change planes, clear immigration or head over to the baggage carousel. Such movement can get difficult without a carrier. Baby carriers are also more compact — with some easily folding up and fitting in a big handbag — and can be taken literally anywhere and used in any terrain. However, carriers (no matter what brand) will eventually put a strain on some part of your body. Whether it be your nape (as is the case with the Chicco carrier) or your lower back (true for my Disney Babies carrier), if you intend on using it for more than two hours, there will be pain. I’ve also tried slings. Same concept, different style. For those, your shoulder will take the hit.
If you have the option, take both. If choosing between one or the other, I’d be more partial to using a carrier.