The engagement is the same in both cases (1st and Reverse), nothing changes mechanically. What is different is that reverse has a taller ratio to 1st (3.4 for reverse vs almost 3.8 for 1st), and there are straight cut gears and no syncro's.
The last 2 shouldn't make any difference aside from the actual process of getting it physically in gear (input shaft needs to be rotating slowly from momentum to guarantee engagement). The slightly taller gear combined with the initial slack in the drive-train that needs to be taken up when going from one direction to the other would probably be the main factor along with the different way that most of us engage reverse, i.e. typically very slowly when in a confined parking environment.
Can you share the particular driving environment where you have the issue?
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