The starting questions are...
- Does this totally new functionality have anything to do with the original app?
- Is your first app priced to low?
- Does it open new markets beyond the original app?
- many other questions to help figure out the best approach
For #1, if it is totally new functionality that does not really relate to the existing app then a new app is the way to go. However, if the functionality is / would be expected as a feature in the existing app then you have to stay with that app and embrace and extend.
For #2, a lot of times when taking a product to market, people don't really do pricing models and when they do, they are overly optimistic about how sales will go and usually X% higher than what they actually turn out to be. This means that since sales are not strong enough to support the company additional money has to be raised, one way is to split functionality out and charge for each part and use the tag line that you pay only for the functionality you need not some full overpriced suite. However, most vendors after they get x number of functionality the combine and make a full product with a full price, it is just a stepping stone. If the price for the first app is too low, will adding the new functionality increase market adoption enough because you must have already figured out that people will not pay more for you app. Or, would it be better to release a new app to attract more people and have more exposure, thus a bigger market and hopefully increased sales for both apps.
For #3, this goes with #1 and #2... can you open new markets, if yes then build the new app. If it will extend your current market, the add to the current app and work on increasing market penetration.