Once upon a time, both Dragon Age III and the next Mass Effect were being built on the Frostbite 2 engine. Actually, it was as recent as last November when Frostbite 2 was mentioned for both upcoming games. However, when Battlefield 4 was announced as using the Frostbite 3 engine, a clamor went up inquiring on the two RPGs. Luckily, BioWare's Aaryn Flynn has confirmed both DA3 and the next Mass Effect -- don't call it Mass Effect 4 -- are powered by the new engine.
Flynn recently posted the following to Twitter:
A brand new engine has a chance to shine on not one but three new games, which should deliver a high level of graphical fidelity in three very different settings. It's interesting to note when Dragon Age III was announced as using Frostbite 2 as a "foundation," which seemed to suggest it'd be heavily modified. Now we know it was in the sense as a stepping stone to prepare for the switch to Frostbite 3. At least the team has had some time to familiarize themselves with the in-house software, so there is that.
Dragon Age III and Battlefield 4 are both due by the end of this year, while the next Mass Effect is still in the planning stages. Battlefield 4 is set for the PC, next-gen, and current-gen consoles, while the other two games are up in the air (and maybe next-gen for DA3). Sadly, Nintendo's Wii U can be ruled out for all three as Frostbite 3 doesn't support it.