The job of a GM is never done

It would depend on the role-play, honestly.

I can understand if, by option 1, the GM is very clearly trying to sift out those who may not be to the level of writing they deem appropriate for their expectations, whatever they may be, with no obligation to go in and explain or correct why someone was not accepted. Through certain wording, the GM frames the responsibility of making an "interesting" character or one of the "best" apps was very squarely put on the shoulders of the applicant. As a GM, this method makes it easier on us because all we have to do is leave the sign ups open and then return to make a final judgement on who "passed", basically. Then we can dust our hands of it on the deadline and move forward.

The downside to this method is players who may not consider themselves "good writers" or consider themselves "new" (to the hobby, the forum, the genre, or even the sense of friend circles that center around the GM) may feel like after seeing someone submit a big CSS-formatted post with many paragraphs and "BIG" words (to quote the universal bane of schoolchildren) that they are inadequate, and already count themselves out. Now there is nothing anyone can do about these people's own insecurities, but the fact of the matter is, this is something that happens and is especially daunting when the role-play sign up is presented like a prize to win.

Option 2, depending on the GM, could be a means to help workshop proposed characters in the event that these characters fail to meet some requirement of the GM for their vision of the role-play. This helps promote an exchange of ideas, further development of sections that may have been rushed or were lacking in comparison to other parts, and checking, correcting, and expounding upon any lore discrepancies. It is still "competitive" in the sense that the person who best understands the GM's intentions and fulfills those wishes satisfactorily first gets the spot, so at times it comes off as a rush to get the GM to help you first.

Alternatively, it may feel to a--we'll say--"sensitive" player that a GM is being too picky, or perhaps the GM truly is being too trivial or domineering in altering a character to fit their desire or idea of "good", if only in a way that it does not allow for the applicant to get their core idea of a character across--so long as it made sense in the first place.

For Cornered On The Market, I've gone with first-come-first-serve. I do not treat my RP as something to compete for, as I take the opportunity to ask questions about applications and hopefully get potential players to start thinking about how their character can relate to the current dynamic, and what unique role they can take to diversify it while still playing to their character interests. I encourage my existing cast to think about the potential in relating their own character to applicant's characters as well. I like to have an open dialogue between everyone, which is something I feel cannot be had when you as a GM hype it into a scramble for a spot on the list.

I'm not going to go into the same amount as detail as Jauntier, but I definitely agree that it depends on the RP. In RPs where you need a small, reliable core of players or with heavy plots it makes more sense to use method one. In larger, more free-flowing RPs though it doesn't matter so much especially as they tend to have a revolving door of players.

I agree with gimmepie, but I am actually split between the two ways much like Disclosed is. I've made use of both, as well as a third option or modification to #2 which is RESERVATIONS. I think I tend to avoid reservations nowadays unless I've pre-arranged my group of players (as with Crossroads). It's just a bit too circumstantial, to let whoever happens to be online at the time the RP goes up, be the one who gets a spot.

However, I also really don't like to have to let people down when they worked hard on a SU, which can easily happen with #1. So if I'm giving it some more thought, I think an option #2 without reservations is the best way to go for most RPs. It's sort of first come first serve, where the player has to make an effort to finish a SU in order to secure their spot - but the GM still has the right to decline them or ask them to change things. As a GM, you simply have to be strong enough to be honest, albeit with a gentle touch c: