I would say stroller, I'd recommend the joolz aer plus, we use it as our everyday stroller now. It's expensive but brilliant.
It depend what you are needing it for? My LO wouldn’t go in a pram since he was 9mo. You could try a sling library? Mine still is in his lovely little frog fabric sling. Great when he is tired and won’t walk anymore. There are toddler slings that look good - I know Tula make them? We also have an Osprey poco backpack (second hand off market place) they are brilliant for longer hiking and dog walking :)
Stroller in my opinion. 13kg is heavy to carry!
Thank you all for your suggestions and advice. My LO stays in his stroller most times but these days he just want to walk. I will definitely check them out 😊
I'm no help sorry but there's a facebook group called Babywearing UK and it's really useful to see others recommendations and advice x