Hello there!
Choosing a new bike! Exciting times!
I opted for the Meteor 350 over the CB350 last year. Having experienced both bikes over a long period of time now, I picked the RE. A friend of mine soon picked the CB350 and since we swap bikes during rides, I do get to ride both bikes very often. I think I will summarize which is the better option so you may make the right decision.
1. Easy of riding: CB350. The weight combined with the slipper clutch and engine characteristics make this very easy to ride motorcycle. True to it's name, the CB350 is a GREAT city bike. The RE has a significantly heavier clutch which I soon got used to. The Honda's slip and assist clutch has bigger advantages as you rightly mentioned. Since clutch control is a prime necessity in bumper to bumper traffic, this should be a significant consideration. My vote still goes for the Honda.
2. Power & Performance: CB350 is the clear winner. It's lighter and quicker, makes more power and torque. The RE is no slouch but it's definitely more relaxed than the Honda. With the RE, you ride the torque wave. The CB350 is versatile, you can ride the torque wave but in-gear acceleration is inferior to the Meteor. If you're in the right gear, the Honda is the clear winner. If you prefer a more forgiving style of riding and changing gears, the Meteor is a better choice.
3. Comfort: Meteor 350 is the clear winner. The seating position is GREAT. I'm ~ 5'7" and on the heavy side. The RE has the wider seat which you technically, sit 'into' instead of on. The forward set foot pegs are not at all a nuisance for someone my height, since you are taller, might sit a bit more knees up. Still, I feel the Meteor is a lot more comfortable while the CB350 has more of an 'engaged' riding position. Also, the Meteor's footpegs do not brush against my shins while paddling through traffic. The Meteor is not at all a difficult bike for the city. The 191kg kerb weight may seem like a disadvantage over the CB350's but it really isn't. Even 'U turns' are easily manageable, especially for taller individuals.
4. Gearing: A BIG reason why I chose the Meteor over the CB350, the RE has better gear ratios, so I don't have to change gears as often while riding in the city. It's just more of a relaxed cruising machine whereas the CB begs you to be in the right gear and is overall a more aggressive bike.
5. Fuel economy: Mixed opinions. Both are very fuel efficient machines but I'd give the edge to the CB350. The meteor is also pretty good. On my most recent 250km round trip, I got 45kmpl and I am pleased with this considering speeds between 70-100 kph throughout the ride.
6. Refinement:

No comparison. The Honda is definitely better. The Meteor is surprisingly not too far behind but I can say that the Honda has far less vibes at higher RPMs. I myself, am not bothered by the vibrations on my Meteor 350, I actually prefer them. At city speeds, both are very smooth machines. At highway speeds, the Meteor has relatively vibey footpegs >90 kph.
7. Sound and character: I personally am a fan of the Meteor. While I agree that the Honda has the louder, raspy exhaust note, the Meteor sounds more natural. Fellow owners of both bikes can confirm: The Meteor sound is even, from both engine and exhaust. The CB350 sounds more artificial with a more pronounced exhaust and not much sound from the engine. Closing the throttle while on the move, the RE sounds much much better the Honda, with a nice guttural rumble from the exhaust and engine.
8. Looks: Based on opinion entirely. I naturally gravitated towards the Meteor. It looks like a proper cruiser, built well, heavy, low and torquey. The CB350 is also a looker but despite the all LED setup, I found the Meteor to look a LOT better.
9. Service: Availability and distance to service networks should be a BIG concern. My service centre and sales office are barely 3km from my home, which was another big reason why I chose the RE over Honda. If you intend to use the very same bike for daily commutes + long rides, occasional service visits are necessary before or after a planned, long distance journey. If a BigWing dealership is near you or is at least, easily accessible, Honda is a good choice. My personal experience with RE service centre has been absolutely fantastic. They go above and beyond. Your experience may vary based on location.
To conclude, there's a clear winner in terms of flat out performance: The CB350. However, I found that the Meteor is a lot better choice for a more laid back style of riding. It is the slower motorcycle than the CB, but is built for a very specific type of rider. Rest depends on individual preference. Mine were comfort, stability, good looks.
Both are fantastic bikes and you couldn't go wrong choosing any of them. Even though I own the Meteor, I would love to own the Honda as well. This, I can say confidently.
Hope this helps you!