the first four times i had the opportunity to combine alkashards, i took the battle items. i’ve not yet finished my Hunter’s Lodge, and the battle items i chose were Hurricanes and Scrolls of Alteration, and each time i was able to combine alkashards happened to coincide with the weeks of Mythic Titans and Ninja Tower. my rationale was that if i were able to compete for top scores in both events, i’d get way better than the 30 emblems or 3* ascension mats would get me. those were fruitful decisions for me.
my most recent combine, i chose emblems because i was provided an option for a class i’m sorely lacking in (Druid) and the battle items weren’t ones i wanted. if you’re sitting on 3* ascension materials because you don’t have the heroes for them yet, then 30 emblems is actually plenty for whatever 3* and 4* heroes you have, especially in conjunction with one or two levels of the emblem quests each week.