No they don't offer both per say. (Double dipping)

I personally selected to earn points because Marriott always runs really good promotions such as Mega Bonus or Double up with Visa... etc. That way you get much more opportunity to accumulate points. Then I usually redeem for a travel package (hotel & air)that includes 7 free nights and airline miles. Example 165 Marriott points will give you 7 free nights at a cat 1-5 hotel and 50K Air Canada/United/Delta/
American miles. You can redeem for more just check the rewards chart.

For more info on this type of reward please follow this link:

http://marriott.com/rewards/usepoint...WT_Ref=mi_left