Rico Neitzel told me back in the days, that during Magento updates files gets deleted, therefore it is a bad idea, therefore you want to run a patch (not the ones from Magento, but a patch between the versions) over your Magento installation.
After fiddeling around for a while it is a good idea to document, what I have just done (I updated from 126.96.36.199 to 188.8.131.52):
Get a trusted git repository with all Magento versions you need, I can recommend https://github.com/OpenMage/magento-mirror
git clone https://github.com/OpenMage/magento-mirror.git
Make sure your current installation is free of core hacks and all files exists which might get patched
magento-mirror$ git checkout 184.108.40.206 (old version) production$ rsync --progress -v -r ../magento-mirror/* .
You might have now too much files - either you have them already in your gitignore - if not, time to add them.
Create a patch file (diff-index is needed for binary patches)
magento-mirror$ git checkout 220.127.116.11 (new version) magento-mirror$ git diff-index 18.104.22.168 --binary > patch.patch
Apply the patch
production$ git apply --binary ../magento-mirror/patch.patch
Now you have a working copy with all the changes. You can review them, commit them, etc.