A composite longbow +2 Str doesn't give you increased Str, it requires +2 Str. Your 8 Str character will be greatly penalized:
All composite bows are made with a particular Strength rating (that is, each requires a minimum Strength modifier to use with proficiency). If your Strength bonus is less than the strength rating of the composite bow, you can’t effectively use it, so you take a –2 penalty on attacks with it. The default composite longbow requires a Strength modifier of +0 or higher to use with proficiency. A composite longbow can be made with a high strength rating to take advantage of an above-average Strength score; this feature allows you to add your Strength bonus to damage, up to the maximum bonus indicated for the bow. Each point of Strength bonus granted by the bow adds 100 gp to its cost. If you have a penalty for low Strength, apply it to damage rolls when you use a composite longbow.
You will thus suffer a -2 attack penalty when using this bow, and a -1 damage penalty.
However, it's a +1 weapon (+1 to attack and damage with all attacks made using the bow).
Overall, this means you suffer a -1 attack penalty and +0 damage, compared to a regular non-composite longbow. In other words, other than the keen property, this is overall worse for your 8 Str character than a normal longbow.