ok, i'm just gonna give a personal rundown on how good i think the individual pheonix lords are in 5th ed, if anyone wants to contribute or discuss anything feel free.
I'll start with what i beleive to be the least effective and work my way up to the best.
Asurmen: Now, i'm not saying asurmen is bad, i just dont think he's very effective. Asurmen is the most durable of the pheonix lords with defend and battlefate but he is rather lackluster when killing stuff, and you get a pheonix lord for his ability to destroy stuff, not for his ability to take a beating, a wraithlord can fill that roll better and be less expensive. asurmen can have up to 5 shooting attacks and 5 close combat attacks, the cc attacks being power weapon ones (the dire sword ability really doesnt do much at all) but they are all S4. i beleive the higher strength attacks of the other pheonix lords are much more useful. all in all asurmen is reasonably good at killing regular soldiers on most armies but other pheonix lords can simply do a better job at it, and since asurmen is the most expensive pheonix lord there doesnt seem much point in taking him, unless you want him to tie up another indipendent character for a long time (and if you want to do that then a fortune farseer with some warlocks would be a better and less expensive choice).
Jain Zar: Jain Zar, like asurmen, is a good model, the reason i dont like her is that most of her abilities just dont do much most of the time. war shout and acrobatic just dont do that much at all. You dont want her to be assaulted in the first place and most enemies on which war shout would be useful have a high enough leadership so as it doesnt bother them. furious charge doesnt do much either, there are very few models in the game that can match her base initiative of 7 so boosting it to 8 doesnt do much. (could possibly help in a sweeping advance but again, 7 is enough usually). the extra strength is also not really neccessary as her S6 attacks are enough to wound most regular models on a 2+ anyway. you could give her an extra attack using her silent death in close combat and furious charge would give her S5 but i think S6 with her regular number of attacks would still be more useful (unless going against tau or guard but in that case it doesnt really matter what she uses, she's going to kill them anyway). Jain zar is decent, but she just doesnt offer anything really special that you couldnt get just by purchasing a squad or two of aspect warriors for the same cost.
Baharroth: Baharroth is interesting, and can be useful, but not because of his ability to kill stuff. When i use him i use him as a harasser and delayer. basically charge a unit, kill a few guys and then either hit and run to get out on your opponents assault phase so you can shoot them on your turn, or skyleap on your movement phase so you can shoot them in your shooting phase. he is rather average in terms of being able to kill things. his gun is rather decent but nothing special and in close combat he's actually the weakest pheonix lord in terms of actually killing things, no bonus attacks or bonus strength. it's also a bit of a waste to try and take down vehicles with him as a single haywire grenade is not that useful in 5th ed as it is unlikely to destroy, or even severly damage a vehicle. I find him best used in his hit and run roll, basically condensing a squad of swooping hawks down into one model that is probably a bit more effective.
Karandas: Karandas is a close combat powerhouse, just like his aspect warriors. Unfortunately he loses 1 attack since power fists no longer can be used with regular cc weapons for the +1 attack bonus but in exchange he can benefit from the outflanking rule since he has infiltrate. Infiltrate itself is nice but being able to come on to the board from a side edge (you can even come directly into your opponent's deployment zone) can be priceless. i've had him come onto the board in the opponent's deployment zone, beat the crap out of a unit of marines and force them to fall back...off the board. they shall know no fear doesnt help much when they are right at the board's edge. he doesnt offer too much more than simply being a close combat sledgehammer, but usually that's enough, his only real weakness, possibly a bad one is that he has to attack last so a unit with power weapons could possibly kill him before he gets to show his stuff. it's nice to run him with a unit of scorps as they can give him a bit more lasting power.
Fuegan: Fuegan can fill one very important roll in an eldar army. he absolutely destroys just about any vehicle he gets near. Firepike, tank hunter, melta bombs, fire axe giving him monsterous creature attacks, he is probably the most effective model in the eldar army in taking out enemy vehicles with the exception of the D-cannon and possibly a wraithguard's gun. With vehicles being harder to destroy he can be a very valuable asset in an eldar army and is one of the few models who has a resonable chance of actually taking down a monolith. But he is not only good at taking down vehicles he is a suberb troops killer. S5 power weapon attacks aside he can also take hits very well from normal troops. feel no pain is for all intents and purposes a second armor save. it doesnt work against power weapons but since most attacks are not going to be power weapons it means he take take a huge beating in close combat against normal troops while dishing out a lot of damage.
Maugan Ra: Ok, this guy is probably the only pheonix lord who is really wasted by putting him with a squad of his own aspect warriors. while he may be the reaper pheonix lord he should definitly try and get to grips with the enemy. his weapon (both ranged and in close combat) is excellent. He esentially has an assault cannon with a longer range and pinning. both fast shot and crack shot can be very useful, fast shot when taking out light vehicles or mowing down light infantry in the open or crack shot against tougher infantry (crack shot is especially useful as ignoring cover caves can be a huge benefit since many armies will be using their troops to gain cover saves and rerolling wounds means you also get a second chance at getting rending on your to wound roll). Maugan Ra delivers more effective firepower than most eldar vehicles since they miss half the time (his BS7 means he hits on 2+ with a reroll of 5+ on a miss). also, once he gets into close combat S6 power weapon attacks will shred just about anything he encounters. I like to run him with a squad of wraithguard as they are both fearless, wraithguard are not aspect warriors so he can join them, they both can move and shoot and while the wraithguard provide valuable protection as he approaches the enemy he provides the close combat power that they lack, a very good combo. He is also the second least expensive pheonix lord which, while not that important is still something to consider.
so, as far as ranking i would have:
asurmen and jain zar at the bottom simply because of their lack of anything really special that makes them worth getting.
baharroth in the middle simply because of his utility in hit and run tactics.
Karandras is third for being a close combat monster and his ability to either start near the enemy or arriving later on in unexpected places. the main reason i ranked him 3rd was because he attacks last which can be very bad in certain situations.
Fuegan in second place as he is a tank destroyer as well as a troop killer. His ability to take out heavy vehicles becomes all the more valuable in 5th ed.
Maugan Ra in first as he can take down just about any kind of troop very well along with light vehicles while at the same time being very nasty in close combat. He is very well rounded in his ability to kill stuff so i find him the most useful in different situations, the type of model i would play in a tournament where i dont know exactly what i will be dealing with.
this is just my opinion right here, i would like to hear other people's outlooks on what they feel pheonix lords can or cannot do in 5th ed. in general they are very inefficient models as far as points but they are damn fun to play with.