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In a progressive HTML5 Webapp, is it OK for the Android Version to have notifications and the iOS version not?
Seems a bit off, but iOS does not allow notifications for webapps.
Should I use an alternative (SMS, Facebook Chat etc.) on both or just on iOS?
A great example of what not to do is Microsoft Word for Mac, where many of the keyboard shortcuts follow Windows conventions. Seems fine for users of one platform, disorienting and annoying on the other.
I don't use both Android and iOS simultaneously as a primary device, so I don't have any hard data on density or frequency of notifications, but you might find iOS users are getting fewer notifications on their devices and therefore you want your app to show fewer messages.
Or, as Dominik pointed out, different platforms have different capabilities. For example, if a handy feature of your app is to take some action directly from a notification, but said feature can only be implemented on one platform, then you may find that the notifications are less useful (or even useless) on the platform that doesn't support the direct action.
If an alternate method would be supported, such as SMS/Facebook, I would make it available to all users. With a PWA you might find many edge cases and reasons users don't want or can't use traditional notifications.
I think this may a little bit depend on the particular business case. However, I believe that in general this is acceptable.
Various platforms have their specific capabilities and limitations, and in some cases the same app may allow something on one, and not allow on another. Fo example, the possibility to present notifications is limited on iOS, as well as running some services in background, accessing some bits of data directly (thinking about my Pebble watch now) etc.
Therefore, I believe it is a business decision if you would want to use on one platform some options that are not available on the other one. As this is a decision between a limited coherence and an unparallelly extended richness of your app.
Referring to the last part of your question, I would suggest looking for a notification system that would be platform agnostic (SMS, email etc) and enabling it on all devices, then adding an option for Android users to switch to something else.
