About 6 months ago we looked at these three as well as some other providers and we chose LP+ for the following reasons:
Based on Microsoft technology, integration with Office which was crutial for teachers, managed service allowed us to have other people developing and managing the platform instead of it falling to us, opportunity to use Outlook, teachers found the product the easiest to use, flexibility of SharePoint, Customisation of the look of the platform, able to use existing office resources teachers had created within the platform, opportunity to collaborate with other schools on LP+ both england and abroad, the LP+ development roadmap was superb (MIS, mobile, parent, community), and we were very impressed with their knowledge around education/pedagogy and how a learning platform fits within a school environment and the challenges we face.
I can say that we were really dissappointed with Ramesys, their product is old, unfriendly and generally needs a complete overhall.
Frog were good and had a really great looking product on the surface, but this is really only a VLE and we were after a MLE. The sales guy was very good when kept within his comfort zone but once we delved down into specifics the functionality/flexibility did not compete with SharePoint and were poor on collaboration if you had more than one school (feeders etc), which was key to us.
Since going with LP+ we have not regretted it and have a good relationship with them, the support is good and we feel we made the right choice 6 months on.