I don't agree that you can't use these words interchangeably. In both of the examples given above, praise and compliment can be used depending upon the feelings of the speaker. Example1, She always receives high praise for her sense of style because she really knows how to mix and match her outfits. (If the speaker feels really impressed about how she dresses, then praise is an appropriate word. Example2: Praising God is like 成語．．．it's a phrase people say, however this does not mean it's wrong or inappropriate to express lesser feelings. If I feel like complimenting God, I can compliment him. These words are used based on the feelings of the speaker, but I do agree that praise is a stronger feeling than a compliment. Other words that can be used instead of praise: bless, celebrate, exalt, extol, glorify, laud, magnify Other words you can use instead of compliment : applaud, cheer, commend, hail, salute; extol, glorify, laud, praise

To my mind, "to praise" someone is to express a higher level of a compliment. It gives someone a deeper feeling that they are worthwhile or loved than a compliment does. There is also a higher chance of compliment being hypocritical (e.g. when a man compliments woman on something in order to get a desired reaction). Praise is in most cases without hypocrisy. I praised him for his dedication and honesty. He's a great person and worker. Vs I complimented him on his dedication and honesty. He's a great person and worker. From your two examples, No. 1 is better, in my opinion. Others may disagree and consider them pretty much interchangeable.

While both of these words basically mean the same thing in a given context, to praise as in: The teacher praised his outstanding ability" is much stronger in meaning, whereas "the teacher complimented him on his work" has a lesser nuance. In addition, both these words have contexts in which the other one cannot be used. For example to praise can be used in a religious sense: "The people praise God" whereas the word compliment cannot be used in this context. On the other hand, "She compliments me on my outfit every day." would not be a fitting context for praise. Hope this helps!