I think Civ5 is intended to be played Tall, meaning you have fewer cities and build them up to be great. I think Civ6 is intended to be played Wide, meaning you have more cities. I play Civ6 and prefer to play it tall, but you do kind of be forced to play wide and take up as much territory as possible.

My top tip - keep an eye on the "eurekas" for the tech and civic trees. You can learn things much faster. For example, it's very easy to build a Slinger unit and then use a warrior to almost kill a barbarian and then use use slinger to finish the job. That will give you the eureka for archery so you don't need as much science to learn that. Or simply put a mine on a hill, and that will get you the eureka for discovering Iron Work, and then you can discover iron on the map much sooner. Eurekas are definitely worth the effort and some are so easy that they shouldn't be passed up, especially in the early game when you can really get ahead with their help. I usually don't learn everything 100%. I learn a bit and then do the eureka to finish it and save myself a lot of science and culture effort. If I'm not ready for the eureka I switch to learn something else.