I have experience with:
Instrumentum
This I had used at school. "Hic est Gaius." It uses the grammatical approach and it's not interesting for 99% of you because it is in German.
Reading Latin
It clearly focuses on reading. It also uses largely the grammatical approach, but targets to natural reading with reading aloud and exercising natural reading. To help reading each unit contains a reading vocabulary with words which don't have to be learned. Because the learning vocabulary is in English I did write them down in a file with German meaning and I used it with a perl script simulating flash cards. The first three chapters are modified Plautus plays, the last three are classic latin pieces. You need at least two books, one with the exercises and one with the texts and there is a third book with solution for many exercises.
I managed to get through one or maybe two units (out of the about 50 units) a week with intensive learning mostly on the weekend.
Lingua Latina
This goes some steps further than LL. It also does do loud and natural reading, but here everything is in Latin. The reduced amount of grammar is also in Latin. The philosophy of LL is to not learn with flash cards and not so much by scientific grammar, but more by reading text. I think is a normal modern language teaching method called TPRS. In LL there are many many books and even some audio and computer CDs and it not easy to get an overview what is necessary and in what order things should be used.
Regarding the computator CDs I can't say anything as I do neither have a windows nor a macos PC. The audio CD is interesting as it contains the first 10 capituli of LL 1 spoken by the author.
Books are there a lot and mostly thin and not expensive. There is Lingua Latina 1 and 2 and there are colloquia and additional texts. LL 1 are custom stories about a Roman family. LL 2 are classic roman texts. For LL 1 I use the LL 1 book itself, the guide, the vocabulary (available at least in German and English), the extended exercises and the solutions. (The solutions are downloadable as PDF.) I think the same is available for LL 2. Regarding the other things I have no opinion.
At the moment I am in capitulum 17. Out of the 35 capituli I manage to do 4-6 a week. More on the early capituli, less on the later. Maybe even less at the end.
Edit 1: The colloquia should be used together with LL1. This is written in Latin at the beginning of the book. This is not helpful for somebody not knowing Latin and beginning with LL1.
Summary
Instrumentum did not help me at school much. Maybe because I didn't really want to learn Latin. I was more interested in burning sulphur when reading about the Vesuv. RL is different, LL even more so. The result of both are I think not that much different. When I reread older units in RL I could read them as nicely as in LL. There might be a difference in learning speed, but it is difficult to compare. For children I am sure LL is more interesting as it shows more of the ancient life and has therefore probably also a more actively usable Latin. But I have a grammar problem with LL. I do not know very well the gender of the learned vocabulary and also not the conjugation(?) of verbs. Is fulgur m, f or n? is it fugio or fugo? (It is fugio, but that's because I learned it in RL. I just do not remember another -io word of third conjugation.) I think here flash cards are better, but I will just stick at the moment with the LL philosophy. It doesn't mean I will change some time back.