As someone who has both a Sproutcore app and an Ember app close to a production launch, I'll take a stab at your questions (re-ordered for clarity). All of the below is what I've observed with no inside knowledge. A bit of it is speculation, so I've enabled wiki mode on this answer, so that more informed people can correct details.
What is history of the split?
Here is what I've pieced together:
SproutCore was created by Charles Jolley's company Sproutit as the basis of their Mailroom product in 2007. Jolley later joined Apple and Sproutcore was used to build the original web apps for Mobile Me. The mandate was to recreate the experience of Mac apps like Mail and iCal, and that effort continues on Sproutcore today with iCloud.
Jolley left Apple and formed a company called Strobe in San Francisco with a vision in part to leverage Sproutcore. The team at Strobe decided that Sproutcore didn't fit many Web 2.0 use cases well enough, and was too much of an all-or-nothing proposition for developers, so they initiated an effort toward Sproutcore 2. The goals of Sproutcore 2 were modularity, and a more HTML-aware approach that would be more accessible to web developers everywhere. Backbone's early traction was part of this analysis.
After struggling to move the Sproutcore codebase toward this vision, the Strobe team decided to start fresh with Sproutcore 2 (internal codename Amber). Charles wrote the core Run Loop and key-value observer code. Yehuda Katz and Tom Dale were the lead Strobe developers on the project. The vision at the time was that Strobe and the community would eventually port over most features and functionality from Sproutcore 1.x to Sproutcore 2.
Strobe business efforts were not yielding hoped-for results, and the company weighed its options, eventually deciding on a acquisition of Strobe talent by Facebook. Before this happened, a number of Strobe employees, including Katz and Dale, split off to form a new company called Tilde.
Tilde decided to continue to develop Sproutcore 2, but change the name (to Amber.js and then Ember.js) and goals of the project. They dropped long-term goals of backward compatibility with Sproutcore. They dropped support for any kind of view widget library and focused on the HTML/CSS use case with tight integration of data binding with the Handlebars templating language.
Since the dissolution of Strobe, stewardship of Sproutcore 1.x has passed from Jolley to Tyler Keating, and the community has re-focused on cleaning up Sproutcore 1.x, which was in an uncomfortable place for a while when the idea of Sproutcore 2 was looming.
What are the effective differences between the two efforts?
The similarities in the projects are that they feature very similar object models. They have similar property, observer and binding systems, too.
Sproutcore includes a library of view widgets like toolbars, list views, grid views, buttons, and theming system, and a focus on defining the view layer via Javascript and absolute positioning managed by the library. It is very powerful for creating desktop-style apps on the web.
Ember has a smaller footprint. It features tight integration with Handlebars. It is an alternative to Backbone for many projects. It aims to provide a standard application architecture for client-side apps and eliminate boilerplate code.
Those differences will likely lead to the frameworks diverging, although there has been some consideration of adopting the same core. In that scenario, Sproutcore would use Ember's "metal" library and perhaps other core libs).
What is Sproutcore's future, where is it going now?
This thread has minutes from the a recent contributor's meetup.
https://groups.google.com/group/sproutcore/browse_thread/thread/aacf00a6047a866e#
The short-term roadmap is to focus on solidifying the marketing materials, demos, and codebase. The team recently released the Sproutcore Showcase. There is general consensus about replacing abbot, the Ruby build tools for Sproutcore, with a Javascript(node.js)-based solution, which is now under active development. There is also a desire for fewer "large" merges of code from companies like Apple and more frequent releases. Sproutcore 1.8 was recently released.
Is Ember going develop to be a complete replacement for sproutcore?
Not likely. The Ember core team has been clear that they have no intention of personally developing those missing features. It is possible that community members may develop those as separate projects -- flame.js is the most ambitious attempt so far. Ember's design choices make it easier to integrate with projects like jQuery UI, so a full replacement may or may not be necessary.
