You're unlikely to find any 3D engines for both iOS and Android for much less than you'd get Unity licenses. The reason being is any decent work in building a commercially viable engine generally requires substantial effort. The value in something like Unity or UDK (iOS only, unless you're a full unreal engine licensee) is that a lot of the hard work is done for you, backed by years of development effort to make a product that simply works.
The only thing I've found which may come close to your requirement (i.e. cheap game engine) is this: SIO2. I've not used it myself, nor have I seen anything made with it beyond the examples in their youtube channel: Youtube - SIO2
You may simply be in the market for a game engine, but beyond that you need to consider the documentation available as well as community and vendor provided support and beyond that the support for asset creation.
If you only want to do 2D then there are plenty of options available including Cocos-2D and variants (Cocos-2DX is based on C++ code and is cross platform).