robinson:
Yes, the field does transform between reference frames, and general situations are much more complicated than a single "stronger/weaker" answer. Gravity couples to all kinds of things, including rest mass, momentum, and stresses (e.g., in fluids, pressure and viscosity). Ziggurat is completely right in all of this--regarding the field, the non-formation of black holes, and his caution against giving a pat simple and short answer, because there really isn't one.
We can, however, have a situation in which the "different strength" of gravity not only has a definite sense that depends on velocity, but actually turns out to be connected to relativistic mass. For a confined collection of particles of charges q, we can measure the effective charge per particle via the average force on stationary external test particle (fit to an inverse-square law). It turns out that for gravity, the effective charge measured in this way varies as Q = qγ, where γ is the Lorentz gamma of the particle(s)--this is exactly the relativistic mass. In general, the exponent of γ is s-1, where s is the spin of the force field, so this is not not true for electromagnetism, nor any other spin-1 force.
But this is obviously a somewhat specialized situation. Relying on relativistic mass is, in general, improper (and actually is improper even here, the result being more or less an accident of the spin-2 nature of gravity).