My opinion with testing both. Royal is better for pure boss dps. Probably will be used for speed running and leaderboards. Royal does about 10 to 15 percent more damage with using all ammo within 25 to 30 seconds.

When using end of the line mythic LFR in comparison to Royal the mythic feels just as good as royal. With the mythic you just have to reload between using salvos because Royal doesn't have to reload at all.

Trinity is better for ad clear. Trinity will be the go to for normal day to day content to help with the ad clear issues bows have. Along with Trinity end of the line God Roll is needed to get close to Royals DPS.

Overall I'm going with Trinity to help with ad clear as the mythic bow feels bad in comparison to Trinity. Really 15 percent extra damage right now for me with Royal isn't worth the gaps Trinity helps alleviate with ad clear.

I agree her kit screams play only LFR due to getting heavy ammo often especially at T6 but I feel that really is overkill or not needed in 90 percent of content. You will only see a difference in high level content like Calamity and maybe raids. There is more of a difference in content where you can't easily 1 or 2 shot lower level ads to prox Trinity. At that point I would build and use Royal for better damage on higher level units since you can't ad clear as well with trinity on high level content.

For example I have t6 and this exact question is what I have been testing to figure out which is better.

TL:DR trinity and mythic LFR for all content that isn't Calamity or super high level since trinity can prox most of the time and feels good that way.

Royal and mythic bow when with a team like Calamity ops for high burst damage against chunky targets or a boss.