I agree with the now-deleted answer from @Jedrek_Mansfield. It's not so much that one is better than the other. The approaches complement one another.
I have had plenty of experience with adults who still have trouble with basic addition and subtraction. Yesterday a student couldn't do 104 - 8 in her head. I showed her that I broke the 8 down into 4 and 4. Of course she knew 104 - 4, and it turned out she could do 100 - 4 also. I don't use the phrase 'number bonds' in a situation like that.
Once in a while I have a student who is willing to put some work into improving their basic arithmetic skills. And then I might mention the term to help them see the concept. I most often focus on the number pairs for 10. Many of my students don't see how to use those to their advantage: 16 + 7 = 16 + 4 (now I've 'made a ten') + 3 more = 23. Practicing breaking a problem down this way can be a tremendous help to students who didn't have strategies for this sort of thing before.
There is a lovely picture book, Quack and Count, by Keith Baker, that uses this concept well, showing all the combinations of ducks that add to 7. “Slipping, sliding, having fun, 7 ducklings, 6 plus 1.” I have long wanted to teach a math for elementary teachers course, so I could get students to make picture books like this for other sums. Years ago, my son was in a preschool and I watched the teacher play a game with them where the squirrel was hiding nuts. Here are 3, something is hidden, now there is 1. The kids loved telling her that 2 were hidden.
If you're interested in how life-changing something like this can be, you might want to read the chapter The Math Haters Come Around, by Tiffany Bearup, in my book, Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers. (You can download a pdf of this CC-licensed book for free. But I believe it's worth the cover price, if you want to read more than that one chapter.)