If I do a mech duel, I use HBS style init so there isnt much chance for a tie as there is no simul damage. Also, the RPGs do HBS style init where you move+shoot/resolve damage, then the enemy move+shoots/resolves damage.
Finally, for those who are familiar with the campaign ops stuff, there is 'combat intuition' and a unit specialization that lets you move+shoot before the enemy does anything, like how HBS does it, but usually there is a condition to it, such as winning init by x on the roll or taking pilot hits to move fast.
For regular games though, I dont use it. Activating and shooting/resolving damage 1 unit at a time works OK for RPG or campaign things with small numbers of units, but it gets pretty deadly in open games, as causing a knockdown on something before it has a chance to move really alters the turn structure. Since we dont balance with tonnage, giving such a big advantage to light mechs isnt necessary with BV balancing I have found.