I had a bit of the opposite experience yesterday that also demonstrates how much better the combat is. I was trying to take an English city that was past a choke point, made even more difficult by a mountain I had to maneuver around. It was during the medieval period so the English had Longbowmen instead of crossbows... which aside from being a big stronger, also have a range of 3 instead of the standard 2. Given the location this gave the English a huge tactical advantage that I wasn't prepared for so despite my superior numbers and slightly superior technology I was simply unable to take the city. I couldn't get units in fast and in large enough number to get passed their ranged defenses. Because of my poor planning and the terrain I had no choice but to pull out of that war.
I had a similar experience last night. There was a small region of desert between myself, India and England that nobody had settled, but when I discovered biology an oil resource was revealed there right next to the English border. Working on the principle that you can never have too much oil, I sent a settler there and claimed the area, but this annoyed the English who declared war on me three turns later. England only had three cities (London, York and Nottingham) and I had a significant tech lead over them (they were using swordsmen and longbows while I had musketmen, cavalry and cannons) so after dealing with their pathetic assault on my new city I decided to march on and take their entire civilization.
What I didn't realise was that they had the Great Wall which meant that my units were slowed down in their territory. Combine that with the increased range of the longbows and it led to a major quagmire because even my cavalry units weren't fast enough to catch the longbowmen who stayed just out of range sniping my units. What followed was a war of attrition where I was fighting to take and hold every single tile on the way to York. I only managed to take the city after my first infantry units reached the front, but by that point 2/3 of my army was killed and I was in no position to march on, so I was forced to settle for peace. It was frustrating in one sense but way more engaging than stack warfare.