I own both, bought N9 16GB earlier then upgraded to 64GB version. I bought 808 about month ago.
Frankly speaking in terms of specs,raw hardware 808 has many aces.
Let me summarise :

808 Pureview
Pros
-- Brilliant Brilliant camera(Stills), You have to try it to believe it.
-- Very good full hd video recording with kickass audio capture.
-- Very good music playback via headsets and speaker. It has Dolby Mobile etc. which actually make huge difference.
-- FM transmitter
-- Very good codec support out of box, I have thrown all kind of files at it and it plays all without any issues.
-- Very much improved Symbian, Belle FP2 it is. Includes better keyboard,browser,usability tweaks(If you are coming from early Symbians)
- Relatively better support by Nokia, updates, fixes etc.
- Nice collection of widgets.
- Better as phone, louder call, ring volume.
-- Better battery life compared to N9
-- Better Nokia Suite Support
-- Very good Microsoft Apps suite, Nokia Maps is better
-- HDMI, USB OTG, better 3G , WiFi reception
-- In India , we get 1 year free Nokia music unlimited service

Cons
-- Its bulky, heavy and kind of hard to handle.(Specially people used to slim touch slabs or smaller phones). Lens cover makes it even more bulky.
-- Build is not as impressive as N8,E7,E6 or even C7. It doesn't feel that great. You have to handle it carefully, Chrome camera casing is very easily damaged. Few users(including me have slight movement in back cover.)
-- Screen is bad to look at with all pixelation. Otherwise okish once you get used to it. No hot swap SIM card, memory card
-- Email is not so good, no notifications.
-- Only one exchange account
-- App support is decreasing
-- Overpriced

N9

Pros
-- Swipe UI. once you get used to this everything else becomes tedious. Smooth navigation, easy.
-- Very nice screen(compared to 808)
-- Nice contacts menu, accounts support
-- Brilliant design, rubber cover fits perfectly. This fits in hand very well. 3.9" doesnt feel big at all. Eye catcher. Curved glass.
-- Very nice community, app support.Something new to do always.
-- Very good Email,IM notifications. Hot swap SIM
-- Decent camera, takes some very good photos(No comparison to 808 though)

Cons
-- battery life is not great.
-- volume during calls, speaker, headsets is low.
-- Basic things like no predictive dialling missing
-- No HDMI, USB OTG
-- Fiddly USB door(Many people have broken it)
-- No builtin syncml support, office docs editing
-- No FM transmitter, Gets warm faster, especially screen
-- No microSD

My main phone is N9 currently and I just dont like to give up.
808 is gone to Nokia Care to fix back cover, I will try to use it more when it comes back.
Despite many cons of N9 , i like it more, It brings joy to using phone.

My advice
-- Go with 808 if you are in doubt, it will be more useful to you, kind of old swiss army knife. Best multimedia phone , I say.
N9 I can suggest if you want to experience Swipe and design and like to be part of community.
Luckily , I have both

Best Regards,
Suyog