I think it will be easier to connect to cloud service. It easier!
They plan to connect the register to your 1S and print checks from there (from there and send to the client) 30 seconds after payment. It remains only sync to bring to mind.
As the site has no physical contact with the client when you pay to give him a physical check is optional, so no matter where You have cash! Simply send a check to the e-mail or text message! The same will work cloud service.
My opinion is that it is better to connect 1C because after paying the checks will be printed in acquiring the operation and you will see that the check made it, just have to catch 1C in this order from THEM and after breaking through the check it automatically sent to the client. It would be better to have THEM a separate cash register to avoid confusion in the change and proceeds. As well of the cons contain the register itself — the cashier must always be online, always!
If the customer is willing to provide 100% availability of cash, al.the power of the Internet and wants to have full control of all the equipment we need to do in 1C. If he needs to just work, less of a headache it is better to rent in the cloud but have often to pay rent !
It is also not clear how to be with already acquired control cash register Bar light 01 f. Would it be possible to integrate it into the mechanism online cash?
If you connect the box office to 1C it makes no difference what it is. Another question what is cheaper for such cases to buy a cash register that does not print checks (these are in the cloud) and not to spend money on a cash register tape which may end in an awkward moment! =)
Sorry for Megabucks and chaotic thinking =(