NXT doesn't really have an offline wallet. Once created, account data is stored in the blockchain and the account is accessible from virtually any wallet anywhere. I'd say there are local wallets and hosted ones. Local wallets run on personal computers while hosted wallets are in the cloud. e.g. wallet.mynxt.info
The closest thing to an offline wallet is a Jay's Vapor Wallet: jnxt.org/vapor
Not sure whether it is up-to-date or is still maintained by the author.
Below are the pros and cons I can think of between using a hosted wallet and local wallet listed in no particular order.
Hosted walletPros1. Instant access. No wait-time for blockchain download/sync.
2. Accessibility. Accessible from practically anywhere.
3. Some online wallets offer other type of authentication than just a long string of password. e.g. pin-based password, username-password pair, 2-factor auth, etc. It is likely that an account created by these services won't be accessible from any other wallets as they have their own database to store pin-password pairs.
4. User Experience. Some wallets have simple features and straightforward user interface.
Cons1. Security and trust issue. It is difficult to verify the security and the integrity of the hosted wallet (or the host, for that matter).
2. Dependency of service. When the service is unavailable, it may lock users out from accessing their accounts. (See point 3 of local wallet's pro's)
3. Centralised. One host, one NXT server, may service multiple users and thus it promotes centralisation.
Local wallet (or default NRS client)Pros1. The integrity and authenticity of the software is verifiable via hashes.
2. Promotes decentralisation and contributes power to the NXT ecosystem by means of forging.
3. Users have more control over the environment it is run on. This may also be a disadvantage if user's environment are compromised.
4. Customisation. Users have total control over the wallet; which version is installed, which plugins to use, integration with other services, etc.
Cons1. Complicated. For some cases, it may be a bit difficult to get started due to user's lack of technical computer skill/experience, software incompatibility, etc.
2. Vulnerabile. User's personal computer may be hostile or infected which may result in account theft. But this point applies to hosted wallets as well.
3. Too many features. The default NXT client has more than just a wallet which may not relevant to the average users. It has a messaging system, assets exchange, digital good marketplace, monetary system, voting, and more. Hence it is called a client.
4. Operating costs are on the users. Rising blockchain size, CPU and memory resource, internet bandwidth, electricity, etc.
I am sure there are many other points I did not mention for both types of wallet. It is all situational, but there you have it. I hope you get a bit of an idea which one is more suitable for you.
Shin
