Is there any difference between electromagnetic wave made by a negative charge and a positive charge? I know the short answer is NO but I think there should be a subtle difference:
Although both have oscillating electric and magnetic fields that are perpendicular to the path of movement of the wave which is result of excitement in the field , the field itself has another component which is parallel to the path of movement for positive charge and against the path of movement for negative charges.
Let me explain in other words: before the charge moves , the field is outward for positive and inward for negative charge. As it accelerates, a ripple gets formed ( at speed of light ) which is our electromagnetic wave , but that horizontal component still exists right before and after that ripple. I don't know if that makes sense or has any physical value! 
 ( maybe this animation can help explain better:)
enter link description here

 A: One thing you can be sure of is that the sign of the charge, and the direction of the field, are arbitrary conventions.  If scientists in some remote corner of the planet never talked to any in the rest of the world, they could have achieved all the same technology and understanding by saying that fields point away from electrons instead of toward them.  (Let's call these remote scientists "Engineers"!)  So really what you are asking is, do electromagnetic waves from electrons affect other electrons differently than they affect positrons, and the answer is, yes they do-- but only in the sense that the sign of all the forces is reversed.  Some of that difference will be simply that electrons repel other electrons, and attract positrons, even before there are any waves, so I don't know how much of that difference you would call a subtle difference in the wave effects, but certainly the wave effects will be 180 degrees out of phase in the two cases-- just because of the sign reversal that is the only real difference.
A: There is a difference in the electric field. One would be out of phase with the other 180 degrees. There has to be a difference, two different initial conditions. 
If you have a negative and positive charge next to each other, and you accelerated them identically, and they were say separated by a small distance (say d>>lambda at first) the EM wave from each, at the same distance for each from the source the two waves would have electric fields going in the opposite direction, I.e., 180 degrees out of phase. Since both waves are outgoing, i.e. The Poynting vector is outwards, the magnetic field is also 180 out of phase. 
You can convince yourself of this from the geometrical animation in your link, or simply from the equations that have, wrt some coordinate system, a Q in there. One positive, one negative. 
You can also convince yourself if you somehow make d <<< lambda (without causing annihilation, or easier, accelerate a neutron that has the equivalent of a positive and negative charge inside, or to say it more correctly can be observed decaying that way), they each will radiate that way, and the two waves, being 180 degrees out of phase, will interfere destructively. I.e., there will be no radiation. 
Of course, the two fields, if not overlapping, simply interact with particles the way they should, no mystery there. 
