my opinions based on a meager experience in species adoptables: 
draw-to-adopt is fun if you have to time to judge and sort thru entries- but depending on how many entries it can also be overwhelming by yourself

flat sales are good for quick cash and usually better for members of the species that have attributes considered "common" just because they'll get snapped up quicker than auctions

auctions are also good! but you kind of have to use judgement on this one- depending on how you think the design will be received you can go for auctioning if you think it'll get enough interest to start a bid war or if it'll stagnate, but you can also fix this with the whole "bidding ends ___ hours after last bid" deal. it also gives more people a chance to get at it. 

OTA is something I've never done because I'm not big on closed species but I do notice that people can offer up some cool stuff when it is done, depending on how badly they want the design. 

hope this helps ;m;