This topic has been discussed a million times here. There is no clear cut answer if you are part 91. It depends upon whether you are following the letter of the law or the spirit of the law. You also have to keep in mind how future employers will look at the time. Is the guy you are flying with an MEI? If so, the best thing to do is to get him to sign your logbook and log it as ME Instruction Received. You say he is an ATP. In the back of my brain I seem to remember there is some provision in the FARs for an ATP giving instruction. Check the regs on that one.
I don't know much about your experience as a pilot but from your post it sounds like you don't have a lot of time. If the other guy has significantly more time and experience than you, lets face it, you are not the PIC, so logging it as such would be dishonest. The best way to characterize your role in the airplane is as someone who is receiving instruction. The time is obviously worth something, so it should be logged. Do your best to log it so that it accuratey describes the time. When you add up your totals in your logbook they should tell an accurate story of your experiences as a pilot.
Without knowing the specifics of your situation, I can't tell you exactly what to do. However, just reading between the lines of your post, I don't think you can go wrong with the above advice.