Joomla and MiaCMS share the same parent codebase, Mambo.  Both projects forked from Mambo, but at different points in time.  Joomla forked from the 4.5 branch of Mambo and MiaCMS forked from 4.6 branch of Mambo.  Many of the Joomla core members helped write 4.5 version of Mambo and many of the MiaCMS core members helped write the 4.6 versions.

Older Joomla 1.0.x and Mambo 4.6.x extensions should work in MiaCMS without too much trouble.  In some cases minor code changes may be required.  Joomla 1.5 extensions will most require code changes to work in MiaCMS since they did a pretty major rewrite between the 1.0 and 1.5 series of their CMS.

To see what progress we've made since last year you should have a look at the release notes here - http://docs.miacms.org/wikka.php?wakka=ReleaseNotes

Hi Brat,

Well, we cannot speak for J! 1.5. They did what they deemed right and honestly nothing actually wrong with it. I hear your pain around  compatibility issues. It doesn't matter if you scream your lungs out, the rationale is, "This is Open Source, and if you're able to do it yourself, awesome. Get it done. Otherwise, go with what's given to you. Joomla!, Drupal, Plone...You name it!"

The story on our side goes;

You know how we split up from Mambo for the sake of saving the code base going totally stale, and adding up a bunch of new features, re-architecting the Javascript layer and all the good stuff. For now, we feel the MiaCMS code base is much more modernized and in a much better shape. However, there is really no point on digging on the 10 year old code base (at certain points) and reviving bits and pieces of it version after version. A major overhaul is required. With Mambo, it was CakePHP. We ditched the CakePHP idea with MiaCMS and steered towards Aliro, which is a CMS framework itself. 
For starters, we know for a fact that a MiaCMS site can be converted into an Aliro site very easily. However, as far as the compatibility goes, this is really up to the 3rd party developers. If they want to provide support for different platforms, it's great. If not, the core development teams usually don't have much to do about those. With Aliro, our plan is to make sure that we cover as many of the necessary extensions as possible. Unfortunately, in terms of existing extensions' compatibility I can't say much about Aliro at this time.

Finally, for MiaCMS as of today, here is a list of compatible extensions.
http://docs.miacms.jp/doku.php?id=compatibility

For extension developers, MiaCMS is probably a better platform than the ditched J! 1.0.x.  Will the third party developers make sure that their extensions work on MiaCMS? I do not know the answer to that one. It's up to the PR machine and extension developers themselves.