Can I expect that a PPA will work the same way it would on a Ubuntu installation?
How can I know that a PPA that works on Ubuntu might not work on elementary?
PPA (Personal Package Archive) are used to include a specific software to elementary OS. Note that sometimes Ubuntu ppas can break things, but this is rare.
The "safeness" of a PPA depends mostly on 3 things:
Who made the PPA - An official PPA from WINE or LibreOffice like ppa:libreoffice/ppa compared to a PPA that I created myself are not the same. You do not know me as a PPA maintainer, so the safety is VERY low. However, for the LibreOffice PPA they offer it on their website. This gives a certain safety net to it.
How many users have used the PPA - For example, if I have a PPA from http://winehq.org, Would you trust it if 10 users have it, and 6 of them say it's bad - and to use the one Scott Ritchie offers as ppa:ubuntu-wine/ppa on the official Wine HQ website. It has thousands of users (including me) that use this PPA and trust that it works
How updated the PPA is - You find out that the last update to a PPA was 20 years ago.. The chance that the PPA will work is close to nothing. The package dependencies that PPA needs are very old and maybe the updated ones change so much code that they wont work with the PPA and possibly break your system if you install any of the packages of that PPA to your system.
On top of that, how updated the PPA is influences the decision to use it. Normally there will be a more up to date version, which is one of the main reasons for having a PPA. You do not want Banshee 0.1 or Wine 0.0.0.1 or OpenOffice 0.1 Beta Alpha Omega Thundercat Edition with the latest elementary OS. What you want is a PPA that is updated to your current OS.
Try to stick with PPAs that are updated to a stable version and not a unstable, testing or dev version since it might contain bugs. An example of this are the daily Xorg PPAs and Daily Mozilla PPAs. These are not suitable for a production environment.
In summary, always look for the maker/maintainer of the PPA. Always see if many users have used it and always see how updated the PPA is. Places like OMGUbuntu, Phoronix, Slashdot, The H and WebUp8 are good sources for PPAs that many users have added and tested.
Some bleeding edge (PPAs that stay very up to date including adding Alpha, Beta or RC quality software in the PPA) could potentially damage your whole system (in the worst case).
And why would you want a PPA? The software in the repositories can lag behind a long way. For example, in the Ubuntu 14.04 Trusty repos, Insckape version 0.42 is avaliable. With a PPA, you can get 0.91, with many new features.
It's also better in many ways than downloading a
.deb file. These never get updated and can have security flaws that won't be patched automatically on your computer.
PPAs are inherently unsafe. By adding a PPA, you are giving a 3rd party the ability to distribute/replace any package (including important security-related system packages), and consequently the equivalent of administrator privileges. You should only add PPAs of developers you know to be trustworthy.
That said, theoretically PPAs that target Ubuntu 14.04 (Trusty) may be compatible with elementary OS Freya. However, there's no real way to know other than by trying it (or if the distributor states that it is compatible), and some differences between elementary OS and Ubuntu could cause issues.
One difference, for example, is the version of GTK+ (Ubuntu 14.04 uses 3.10, elementary OS Freya uses 3.14). elementary OS also includes several newer or patched packages; for a complete list, see the os-patches PPA on Launchpad.
Adding a PPA made for Ubuntu 14.04 by itself won't bork your install, but suppose you install some applications which need to install some dependencies.
These dependencies may be unable to be installed without uninstalling some packages essential to elementary OS.
(Ubuntu) Software Center doesn't help with this, as it usually doesn't explicitly tell you what gets installed and removed. I would recommend installing Synaptic Package Manager if you plan on installing from 3rd party PPAs as it will tell you exactly what happens on a package installation. (or you could use apt-get...)
A good rule of thumb is to look very carefully at what an installation does before installing, and if it wants to remove packages then don't install it. Look up what the packages are first and make sure they aren't elementary OS system components.
Most PPAs made for Ubuntu won't bork your install (many won't even ask to remove packages), but it only takes one...