Eh, I think NG+ without levels/equipment/whatever but a full party is more fun. I've done both and I simply enjoy having whoever I want right from the getgo more. Early game might be odd due to many of the non-starting characters having extreme SP costs to their "cheap" spells, but then again you aren't supposed to have 12 characters then either so it more than balances out. Youmu is kind of a lame luck-based fight if you do her at a natural level (reimu 9 IIRC, 11/12 is what happens if you grind a tad IIRC) in a proper playthru too imo. I mean if she decides to spam wind karma, you're pretty hooped regardless of your planning/strat. Or if her ghost ally does aoe poison very early, it is also pretty unfair, particularly because you have no means of curing, or even seriously boosting resistance to it early game.
But anyway, some people were talking about Patchy's usefulness. She's very useful from start to finish IMO. Silent selene is always a great spell with its high pierce, high damage, non-element, and good delay (not counting patchy's slow speed that is). Her high MND far outweighs her low hp and def for most fights, someone mentioned composite attacks, her mnd should be so high that she'll tank composite attacks better than everyone but your pure tanks too. Though sometimes if you fail to defense buff with reimu/yukari/ran/whoever first, what would be a composite attack which deals 0 to her might be a 1-shot later. As for physical bosses, it's true, she's an accident waiting to happen if a boss has thousand needles or arrow rain. But fortunately most with thousand needles use it in a predictable pattern, arrow rain is a 50/50 affair in +disc though. But honestly, I play defensively, and I like to clear the game at low levels. Truth is, most, if not all nukes, not just patchy, are often 1-shot by SOMETHING or another from most serious boss fights. The game gives you 12 characters to use in a fight, with only 4 duking it out at once. You can play 0-casualties hardcore mode if you like, but making educated risks using your characters is just part of winning imo.
As for tier listing, I'm sure many of you know, but I still think that a tier list is kind of silly in this game. There are so many characters, and so many combinations of them. Then there is your playstyle, level range. etc... Sakuya for example is flat out terrible if you're underlevel against a boss with even slight levels of defense, but if you're overlevel, or fighting something with no defense, she's a beast. Yukari is also likely awful if you have reimu or ran and/or kaguya. But if you have none of those, she's most likely going to be one of your most important characters for any difficult encounter. I personally have bias with my own opinions on characters in the sense that I pretty much always have china, Reimu, Remi, and Patchy. Between those 4, there is nothing I can't damage AND survive for a long ass time against. I like playing defensive, and those 4 can pretty much endure everything, minus patchy against arrowrain/needle enemies. China can heal herself, Remi can def buff herself if Raymoo needs to heal while def buffs are "only" at 30% or below .
That's kind of my problem with this game. I love it to bits, and I like experimenting with parties, but I pretty much nailed down the optimum party for my playstyle (aside from those 4, I feel like I'm gimping myself if I'm not including Ran, kaggy, Nitori, and Mino...Though I haven't played since it was discovered that Iku's buff was 70%...not 35% like the wiki originally listed, I MIGHT be able to replace ran with her, but I do make use of ran's def buff too so I dunno).
As for Eiki, I found her to be very useful the time I used her. Her damage is obviously good. Yeah her trash clearing options are limited, but defense ignoring is actually pretty useful for SOME trash...you know, the really really annoying kind that are otherwise the kind that might make you decide to just flee from instead.. But more importantly, she's one of the beefiest top-tier nukes in the game. Her MND was fantastic, and her hp wasn't shabby either. Best of all, BECAUSE she ignores defenses, you can forfeit spending level up bonuses to her atk, and the "gimp" factor won't be as bad for her since its effective damage from 0 is so much wider due to defenses not eating her atk up...err.. I can't explain it well. I'm sure some people who aren't real theorycrafters will think I have it backwards but I don't >=P. But yeah, again, defensive stats on a nuke aren't really a turn-on for many people, so whatever.