Well, there doesn't need to be any math to tell what's plainly visible. The rift line is cheaper than the raid line but it's also weaker. That's plain there and there's no question about it. You trade cost for power. The subject of the thread is mostly on how a newbie with absolutely nothing should start up their gearing process. An experienced player can do ample amounts of DPS with even the lowliest of setups because they know the class, the game, and how to keep up. A newbie who can barely keep up with a rotation, much less with the changing aspects of how a dungeon boss fight goes, would not be as efficient. Even the easiest one star dungeons can force a drop in DPS if you are too new to avoid all the knock downs and holds most bosses down there still do. Add in the still existing one shot attacks some of them do (iron monkey for example) and a newbie's dps will be on the floor most of the time. Based on my own experience, even at raven 3 with all else coming from story, a newbie won't be able to break the 100K dps mark. They will need at least bracelet and glove and some sort of rotation to do so.
Add to this, than an experienced player will hurry to obtain and upgrade accessories instead of weapon, so they can go the cheaper rift option without losing much dps. Maybe they will get help from a more geared alt with resources, or from clan friends. A newbie has to form all this from scratch. And that's where experienced have to step in newbie shoes to see again what being a starter really is. I take myself as an example. Even though I've been around this game nearly since it started, I never really did end game, just doing story and leaving until a new chapter arrived. Lately for the first time I started to go semi serious, doing at least the starter dungeons and stuff. Still I'm in my formative stage (and also gearing several alts at the same time to at least an usable stage), so my dps is still not what it may be if I was better trained or if my character had the defacto correct talent setup (I haven't even bothered to look for those). This means that even with similar or even better gear, I won't do more dps than a trained, efficient player. I can now maintain 200-250K on my main, and around 100-150k on most of my alts, with higher bursts. But I suppose my character could easily do much more with the gear it has. Most newbies, until they learn (should they aim for that), will be in a similar position to mine. So don't expect a raven 3 nor a rift 6 newbie to pull 200K dps just because you as an experienced player can do it.
So in the end, if anything, I'd start recommending, instead of getting this or that weapon, to work on learning how to play the character, getting their talents where they will do the most good, and obtaining accessories. This thread has proven that in the right hands and with the right backup, both weapon lines can do well. When I first started gearing up, I farmed Refuge to get the raven material for my raven weapon. I wanted the buffs they gave to use them as an early crutch and I don't mind farming a new rift weapon on the side if I need to. Anyway, that was around 3 days of bud daily farming. But when I discovered such a mat costed a pedestrian amount of gold at F5, I decided to farm for bracelet first and just buy the raven material when I started gearing my alts. Now all of my characters are at raven, and I left the weapons there for the moment while I get accessories for all. As stated, all my characters already do at least what I want from them. So from here I can only go up, even if slowly.