My choice would be the LCP, but the price you mention is higher than our experience around here. They are in short supply and some retailers have tried to get that high a premium, but if you are willing to shop, you should be able to do better.
I chose the LCP primarily because the fit and finish of the LCP is superior to the P3AT and the reputation of Ruger for customer service is very high. There has been a voluntary recall on the LCP and they have handled it extremely well. Much more information is available at the forum devoted to it. Elsie Pea Forum - The #1 Ruger LCP Owner Forum and Information Source
I have the P3AT and paid $259 for it. Thus far I have 500 rounds through it without any type of failure. I am on a waiting list for a LCP and frankly am not sure I will purchase it when the call comes given the performance of the Keltec.