In general, Dalton has more comprehensive background information, while the Lonely Planet book is better with the practical information. Dalton does have more on out-of-the-way villages and the back-country, but some of this is unreliable — he claims, for example, that you can hike from Mt Anjasmoro to Mt Arjuna along ridge-tops, although there is a 1000m deep valley in between them! I suspect Dalton knows more about Indonesia than any of the Lonely Planet authors individually, but he can't manage the same breadth of coverage and varies a lot in his depth: for some areas he provides just a short paragraph of what looks like second-hand information; for others he provides such extensive detail that it is clear he has been there many times. (None of the six authors of the current Lonely Planet edition were among the five authors of the second edition, but some of the material is the same; the work really is a large-scale collaboration.) I can hardly claim to have tested a large part of either book, however, and this evaluation is based solely on two trips to Java and Bali and one to the Nusa Tenggara, combined with some knowledge of Indonesian history and anthropology.
Overall there's little to choose between the two guidebooks. Whichever one you decide to take, I'd recommend reading the appropriate bits of the other for an alternative viewpoint. (While the two volumes usually agree on the hard facts, they often differ in their evaluation of the relative merits of hotels and places to visit.) Another possibility would be to crib from both volumes and take neither, which is what I now do. This is much better weight-wise, as both volumes weigh well over half a kilogram. First-time travelers without decent Indonesian will find a solid guidebook reassuring, however — I can still remember clutching mine on my first trip — and if there are two or more of you and you are planning on spending a lot of time in different parts of Indonesia it might be worth carrying both.
I'm eagerly awaiting the day when you can obtain personally tailored guidebooks — where you specify that you are going to visit Java and Sumatra (but not Aceh), that you are a budget traveler and only interested in cheap places to stay, that you are interested in mountain climbing, and so forth, and are sent a postscript file with just the information you want. Checking out the web pages for Moon and Lonely Planet, I wouldn't be surprised if they have something like this working in the not too distant future.