I would rather have 3 Chase "miles" than 5 ThankYou points, because the Chase miles are convertible 6000:5000 to BA miles, but that may reflect our travel pattern.
Yeah, everyone does what is best for his/her own situation.
It does cost much more BA miles for the same award using AA miles on almost all awards. Intra-Europe takes 20K BA miles but only 10K AA miles for example.