MIT is the most recommended permissive licence: short and very popular (probably the most used worldwide). OSI states it is supported by a strong community. Basically, you can do whatever you want as long as you include the original copyright and licence notice in any copy of the software/source. Another version MIT-0 does not mention the obligation of including the copyright notice. MIT is one of the permissive licences to be used (authorised) by French administrations.
Apache-2.0 is a permissive licence. For OSI it supported by an important community of developers. You can do what you like with the software, as long as you include the required notices. Compared with the MIT, recipients receive a patent licence from the contributors of the code. Applicable law / competent court are not specified
MPL is a reciprocal (or copyleft) licence that is interoperable and - to a certain extend - compatible with other licences, even copyleft or proprietary. OSI states it is supported by a strong community. The recipient must make the source code for any of distributed changes available under MPL, but can combine the MPL software with proprietary code, as long as the MPL code is kept in separate files. Version 2.0 is, by default, compatible with LGPL and GPL version 2 or later and with the EUPL (and the reciprocate is true in this last case, since MPL is listed as compatible by the EUPL). You can distribute binaries under a proprietary licence, as long as you make the source available under MPL. Jurisdiction fixed where the defendant maintains its principal place of business. MPL is one of the reciprocal licences to be used (authorised) by French administrations.
European Union Public Licence, Version 1.2 or later (EUPL)
Official Licence of the European Union (EC Decision, part of European law). The licence is interoperable (no restrictions on linking in order to facilitate the integration of multiple components), reciprocal (third parties distributing improvements or derivatives must publish and provide back the modified source code) and compatible: no global relicensing permitted, but the source code could be reused in other projects under GPL/AGPL, EPL, LGPL, MPL, OSL, CeCILL, LiLiQ. EUPL covers SaaS / network distribution. EUPL covers "the Work" (software and ancillary data). Original in 23 EU languages. Replaces EUPL-1.1 for works "Licensed under the EUPL" without specifying licence version, or adding "or later". Applicable law and court: licensor seat in EU (or specific additional agreement), otherwise Belgium. Support from the Joinup.eu community. Free legal support provided.
GPL-3.0 was forged in 2007. It is a copyleft licence. OSI states GPL (without indicating version number) as supported by a strong community (the Free Software Fundation - FSF). You may copy, distribute and modify the software as long as you track changes/dates in source files. Any derivative including (i.e. via compiler) GPL-licensed code must also be made available under the GPL-3.0 along with build & install instructions. Adding "or later" is recommended by the FSF to cover an hypothetical GPL-4.0, but still means "GPL-3.0 only" for the time being. Therefore licensing under "GPL-2.0 or later" will better improve compatibilities, because the use of the GPL-2.0 is still more important. Compatibility / interoperability are known sources of tension when a project combines the covered code with non-GPL sources from other stakeholders, because according to the FSF linking other software to GPLed works extends the GPL coverage to these other programs.