The 8AX has 110 lumens for 50 minutes (on a good B90) iirc, (I have one, an 8X), while the 6P with rechargable conversion uses the 60 lumen P60 lamp. I'm not sure but I don't think you can use the P61 with the B65 battery stick. It used to require a separate lamp, but now it can use the P60 I believe. I'm sure someone here more knowledgable than I will provide more details. It's all on Surefire's website as well. the length and weight will be less than the 8X series, I think.
The 6P also has a good fit in a clenched fist, like a roll of quarters, not that I've used it that way yet, but just in case a situation hasn't escalated up to firearms level, it's good to know. A 6P with an A19 adapter, making it a 9P with 200 lumen capability, is a powerful deterrent also, and can be used as a kubatan with some training. The 6P is a very versatile platform, upon which you can customize for various needs as they arise. You can add an M2 bezel for shock isolation and weapons mounting. A 6P with an A19 adapter, P91 lamp, and M2 bezel with TID makes a good nighstand light for use with a firearm.
Actually, I really like my 8X too (with tipoff beamshaper) and I use it nightly to walk my dog. Trouble is, you have to change out the battery everytime before you use it.