If you want to stay within the Royal Enfield fold, you can look at the Hunter 350, which will feel much more manageable and comfortable than your older Bullet. But if you want to get a new version of your bike, the base Battalion Black and Military variants of the Bullet 350 will fit in your budget.

The latest Bullet is a refined, comfortable and reliable machine which should return decent fuel economy, when ridden sensibly. Do bear in mind that with the Hunter, you will get dual-channel ABS. But the Bullet's base models only come with single-channel ABS and a rear drum brake. 

Alternatively, other options from reputed brands worth considering are the TVS Ronin, Apache RTR 200 4V, Honda CB300F, and Bajaj Pulsar N250. These smaller bikes will offer similar performance to the RE 350s - if not more - while being more fuel efficient too. 

Take a test ride of these machines before you make a decision. 

Within your budget, you should look at bikes like the TVS Ronin, Royal Enfield Hunter 350, Honda CB350 and Triumph Speed 400. Of these four, the Speed 400 will be the fastest, but it also offers a good level of comfort and usability for daily use. Its tractable engine, short gearing and light clutch will make it a good city companion. 

The other three bikes are more relaxed in their nature but will still offer a tangible step up from your old Hornet 160, especially in the comfort they offer you. 

Take a test ride of these bikes to see which one suits your riding style best before making a decision. 

Both bikes you have considered are good for a beginner rider. The Honda CB350 H'ness will feel like a more spacious and larger machine than the Hunter, which will be a good thing if you are a larger rider. 

On the flip side, with its smaller size and 17-inch wheels, the Royal Enfield Hunter 350 will feel more agile and flickable in city traffic. Do bear in mind that coming from an Activa, both these bikes will feel quite heavy, weighing 181kg.

Something that will be similar to a ride but substantially lighter will be the TVS Ronin, which weighs 160kg. We recommend you take a look at the Ronin instead of the two 350s. Even though you are familiar with how to operate a clutch and change gears in a car, on a motorcycle, it is a different ballgame. 

Do take a test ride of the machines you shortlist before you decide. 

The Harley-Davidson X440 will be a good starting point for a novice rider, although you will take some time to get used to its weight. Since you are shopping in this class of bike, other options to consider are Royal Enfield Hunter 350, Honda CB350 trio and the TVS Ronin. Of these, the Ronin will be the lightest and one of the most affordable options while still delivering comparable performance to the 350s. 

The Yamaha Aerox 155 is a good scooter in many ways, but its stiff rear suspension and cramped ergonomics for taller riders are two big reasons we would steer you away from it. If you do want a large-capacity scooter, then the TVS Ntorq 150 is our current pick because it has engaging performance but doesn't sacrifice comfort or practicality. 

Take a test ride of everything you consider, which will help you decide if you're ready to get into bikes or should stick with a scooter. 

Considering your requirements, the options we would recommend you take a look at are the Bajaj Pulsar N250, TVS Apache RTR 200 4V, TVS Ronin, Honda CB350 and Royal Enfield Hunter 350. Of these, the lighter 200s and 250s will feel more agile and have better fuel economy, while the heavier 350s won't feel as agile but will be a little more comfortable. 

Another option worth taking a look at is the Hero Xpulse 210, which will be the most comfortable of all the bikes listed here. However, it won't be as agile owing to its large 21-inch front wheel, soft long-travel suspension and long wheelbase. 

There are also some instances of engine issues being reported online, so it would be advisable to wait for some time before purchasing the Xpulse.

A test ride of these bikes should help you figure out which is the best option for you.