I'm not a professional by any means, so please excuse if my explanation feels a bit subjective. Suitability, to me, is kind of an binary attribute. Either something is suitable or it's not. If even one requirement I have is not fulfilled, I'd deem the flat unsuitable. And as it's binary, the phrase 'more suitable' doesn't seem right.
Personally, I feel that convenience goes a step further, semantically. I don't compare flats in terms of convenience if they aren't suitable in the first place. Convenience is about comfort, so quite a bit softer than suitability with its connected hard requirements. Maybe you'll get my idea but to be sure, I'll give you a short example.
I'm looking for flats and my requirement is, among other things, commute under 30 minutes to work. I have to offers with one having 25 minutes of commute and the other having 10 minutes of commute. Both are suitable, but one is certainly more convenient than the other in terms of commute.