If you limit the discussion to carbon steels, the strength of the weld and heat affected zone is influenced by the cooling rate from the austenizing temperatures to ambient [OK, to the Ms line (temperature)] all other items held constant.
Very simply stated, for a given amount of carbon (or alloying elements that increase carbon equivalency), the faster you cool a piece of steel from high temperature (where the steel is fully austenized and all the carbon is in solution), the harder and stronger it is.
Using low heat input while welding (stringer beads, low amperage, short arc length, small electrode diameter, no preheat, etc.) the faster the molten weld metal and heat affected zone will cool. The results is a hard, strong, brittle weld. Again, how hard, how strong, how brittle is a function of the total carbon (and other alloying elements contributing to the carbon equivalency) and the cooling rate. Interestingly, how fast the piece is heated isn't a factor.
Try this experiment. It is quick, easy, inexpensive, and it will show you the relationship that I'm talking about in the preceding paragraphs. Make a T-joint using 1/2 inch thick A36 (or A572, what ever is handy) and weld two samples. The first T-joint should be welded in the horizontal position using three stringer beads to produce a 3/8 X 3/8 inch fillet weld. Then, weld the second T-joint in the vertical position using a single weave bead making sure you don't bridge the root. In other words, weld two fillet break samples as shown in AWS D1.1. Remember to weld only one side of the T-joint. Secure both samples to something solid and break the fillet weld with a sledge hammer. Count the number of hammer blows it takes to fracture the fillet welds in each case.
Remember, to be a valid comparison both welds have to be the same size and both have to pass the visual acceptance criteria of D1.1 and both have to have fusion at least to the root of the T-joint. I suggest the pieces be saw cut so you have a good fit, i.e., no root opening.
Tell us your observations at the end of the testing. I know what it will be before you start, but it is best if you find out for yourself. The test will work with either E60XX or E70XX, I suggest using E7018.
Best regards - Al