I was surprised to see that the dictionary definitions of these two adjectives are so similar, but the examples given for each are in line with how I am used to seeing them used in context.
Experiential tends to be used to describe things like training or learning - things that perhaps 'intangible'. I've seen experimental theatre described as 'experiential' where the production invokes a more sensory experience rather than simply observing it.
Empirical tends to be used to describe things like data or evidence - things that are more tangible in that they have been found and recorded.
In your first example, 'knowledge' could be used with either. This ngram shows usage of the terms 'experiential knowledge' and 'empirical knowledge'. Both terms can be found in online dictionaries.
I don't feel that either fit your second example at all. The subject is 'grammar'. Grammar is a set of rules, a structure. It would not be described as either experiential or empirical - how does one experience grammar? You could perhaps describe a study or knowledge of grammar as "experiential" if it was rooted in practical learning rather than the learning of theory.