Lol everyone always wants to know which bow is "best". Truthfully there is no such thing. Basically what i'll do for you however, is i'll break down each bow for you, pros and cons, and hopefully that will help you make a choice if you haven't already.
Strong Bow: Hmmmm how I hate the strong bow yet I would ultimately recommend this bow as your archer's choice. This bow offers the most versatility being that it only takes up 1 slot allowing you to choose any 1 slot weapon while still enabling you to equip 2 quivers of your choice of arrows. The bow has good short-medium range accuracy with minor arrow drop. The bow also fires extremely fast in comparison to a long bow.
The biggest downfall to this bow I feel is its lack in damage, especially when not heirloomed or without heirloomed arrows. Of course in the end an archer is a support class not necessarily suppose to be top listing on every map as opposed to just wounding and stunning enemies creating a whole world of hell for them. I also really dislike this bow because in my opinion it's just extremely easy to use and for the simple reason that about 80% of all archers use it. Once again though I would still recommend you start out with this bow until you get good at archery then venture into using the higher level bows which in my opinion require a little more skill level to use effectively.
War bow: My secret love, I used to love this bow up until the most recent patching where chadz in all his wisdom made it a 2 slot bow aswell as made it hideously ugly to look at aswell. After the skin change I felt as if I was using a giant twig to fire arrows. The bow however does substantial damage and also fires at a fairly fast speed when compared to a long bow. The bow also has very little arrow drop making it extremely effective at medium-long range. I still standby this bow and consider it the bow to use if you want the balance between damage, speed and accuracy. The bow in my opinion also offers the most quality shots and will allow you to feel like a sniper if used properly.
The biggest downfall for this bow for me is the 2 slots it takes up and the lack of damage when compared to the 2 slot long bow. In reality as an archer you're going to want 2 quivers of arrows and that leaves you without a decent 1 slot weapon rendering you totally useless if you get stuck in a melee fight. Also once again the bow is ugly as sin. So as much as I hated to hang up this bow I felt I had to being that it was just too sub par when compared to the strong bow or long bow.
Long Bow: My recent, personal choice of bow. This bow packs a serious punch of Peirce damage when added in with some decent power draw. If you're looking to score some 2-3 shot kills unheirloomed then this is your bow. Hit someone with an arrow or two from this bad boy and they will be hating you or possibly laying face down in the dirt. The bows damage is by far better than that of any of the bows mentioned above and allows you to take down nearly any target, heavy or lightly armored.
The downfalls for this bow though are many. The bow at times feels so slow it wants to make you cry. The accuracy on this bow is also very poor so you honestly won't be able to utilize it effectively until level 30. Also with this bow you want to avoid archer vs archer fights at all costs being that you are stuck with a much slower firing rate when compared to other archers. Once again like the war bow this bow is a 2 slot bow basically rendering you useless if thrown into a melee fight situation. So until you become an experienced archer and learn the ins and outs I would avoid this bow, but I do recommend you try one out for a little bit if you stick with archery long enough to reach level 30.
Anyway, sorry for the long read. Hope this at least helps you out a little bit in making a choice.
Poll