A full answer here has several parts. First, at the time of writing it's important to bear in mind that ConTeXt is not only available but works well, while LaTeX3 is a concept which is being developed. That means that it's not even 100% clear what shape LaTeX3 will take. It's also not clear that LaTeX3 will deliver, but for the purposes of answering the question I'll ignore this! I'll also highlight what seem to be (broad) similarities.
There are then two broad areas to talk about: the user 'experience' and the implementation. In both areas, there are differences but I'd like to highlight one important similarity: both ConTeXt and LaTeX3 are ultimately TeX-based. A radically-different approach from either would be to parse input using another language (Python is often highlighted, for its scripting ability), then convert to TeX primitives (plus low-level macros), and only do the real typesetting in TeX. Neither ConTeXt nor LaTeX3 do that.
At the user level
At the user level, LaTeX works with the concept of a document class as a key concept, .i.e. you always have:
In LaTeX2e, the separation between a class and adding code is somewhat diffuse. The idea for LaTeX3 is to make 'design' and 'code' separate areas, and so have the document class as a purely design concept. ConTeXt does not enforce the idea of a loading a particular 'style' for a document in the same way (although it is possible to load a module to set defaults). There is a key philosophical difference here, as ConTeXt is in many ways closer to the plain TeX concept of 'author as designer', while LaTeX3 is intended to enhance the separation of the two roles.
An area where there is clear similarity is that LaTeX3 will make a lot more use of keyval input 'out of the box' than LaTeX2e does. This is very much a similarity to ConTeXt, which makes extensive use of keyval. There are, however, differences in implementation (the classic one is that LaTeX keyval input skips spaces around the
=, while ConTeXt does not).
Another similarity in this area is that the scope of 'core' LaTeX3 supported ideas is intended to be much broader than 'core' LaTeX2e ones, and thus similar to what ConTeXt manages. Quite how this works out depends on the development of LaTeX3, do it is not possible at this stage to give a more detailed analysis of this area. This area encompasses the 'limitations of LaTeX2e' part of the question. For example, ConTeXt can do proper grid typesetting, which is a significant challenge in LaTeX2e.
At the implementation level, ConTeXt (Mark IV) uses a mix of TeX and Lua. On the other hand, LaTeX3 is (currently) dependent on e-TeX plus the
\pdfstrcmp macro (or equivalent functionality), and thus works with suitably recent versions of pdfTeX, XeTeX and LuaTeX. LaTeX3 then constructs a programming language of its own ('expl3') using the require TeX primitives. This is clearly a fundamental different, as Lua provides ConTeXt with a flexible programming system and also access to TeX internals that are not available using primitives. At the time of writing, it's not clear how LaTeX3 might handle 'LuaTeX-only' ideas: might there be team-supported 'LuaTeX-only' modules, for example?
The fact that LaTeX3 uses only TeX, whereas ConTeXt uses a large amount of Lua, leads on to the fact that LaTeX3, like LaTeX2e, is intended to be a TeX format which can be used in a 'classical' manner
pdftex "&latex3" <myfile>
ConTeXt, in contrast, is a more 'dynamic' assembly as the Lua part is not saved into the format file. Thus ConTeXt is always executed using the
context script. Using this script-based wrapper, ConTeXt can deal with multiple TeX runs, indexing and so forth 'automagically'. The intention (at present) is that LaTeX3 will work in the same way as LaTeX2e: one LaTeX run = one TeX run.
ConTeXt is build explicitly on TeX and Lua, while LaTeX3 defines its own language, expl3. Thus programming ConTeXt means programming in TeX, which is not documented formally in the ConTeXt manuals. A key driver behind LaTeX3 is the idea that beyond the kernel, everything needed to program LaTeX3 should be documented in the LaTeX3 documentation.
LaTeX3 is also aiming for a clear separation between user functions and internal functions, i.e. for every document-level function
\foo there should be a (documented) internal function
\int_foo. ConTeXt has a very rich set of interfaces, but is not (to my knowledge) built on quite such strict 'two-layer' principles.