Both BR and HD-DVD are 1080p (I think 24sf, but not 100% sure) on the disk. On the other hand, like most have said there are very few that accept 1080p and most likely for both camps it will be outputting to the display 1080i over HDMI.

NOTE 1: for HD-DVD the only stand alone player so far announced at all is the Toshiba, and that one will not output 1080p, from what Toshiba said at the time - then again at that time they also said it will come out this year early fall. So that might be where the idea that there is a difference between BR and HD-DVD comes from

NOTE 2: for BR and HD-DVD and anything that uses AACS or is AACS compatible, there is a "feature" called ICT (image constrain token) this is set by every studio on content basis. If set to off then the player will treat all outputs the same, if set to on then if the output is encrypted (like DVI+HDCP or HDMI) then you get full resolution (1080i or p depending on the player) but if the output is none-encrypted (DVI, analog) then it will down rez the video at some point* before leaving the player

* some point because there is noting in the spec that a player manufacturer cannot scale the picture after it down rezed it