Is the wrong antenna worse than no antenna?
There is no way to tell from the information you have given.  How well a system works at one of 433 MHz or 915 MHz when "tuned" for the other can vary greatly.  If this tuning (whatever that means) is highly resonant (high Q), then performance at any other frequency could be very bad.

If it is known up front that a system must operate well at both these frequencies, then that could be to reasonable levels of good enough.  A antenna could be designed that is effective at both frequencies, although it won't be very selective on receiving.

Take a look at the electronic parts that are changed between the two versions.  If these involve components of a resonant circuit, which they probably do, then only experimentation will tell you how well it will work off frequency.

I don't think there is any inherent advantage of ASK versus FSK other than the general features of each of these.  Each will still be a relatively narrow band signal, so the spectrum won't be a issue.

As for signal "quality", I don't know what you mean by that.  Ultimately everything is quantified by signal to noise ratio.  A 433 MHz narrow band ASK signal is just that.  There is really no measure of "quality" to apply other than ultimate demodulated signal to noise ratio.  This signal to noise ratio is dependent in large part on received signal strength, but also dependent on other factors like received strength of other noise sources and amplitude above the inherent noise floor.  Again, there are too many possible ways the circuits could work to give a meaningful answer from this simple outside view.