Depends which cart as well.
Highest is pretty much going to be the enhanced flash carts, for which most mean the DSTwo, ISMM and iplayer. These most will note as having a human noticeable impact on battery life. On a reasonable quality battery then you are probably still going to have your day out and charge in the evening though.
From there it varies, if you are looking for it you might see an effect but it will largely get lost in the noise -- if you are playing it during downtime then whether you have more or less one day then changes what goes. It might also vary enough between games -- get something hammering the CPU and 3d aspects and it will be different to a thing tightly coded to sit there and sip a tiny bit of CPU only when necessary while chucking around 2d sprites. Not seen a patch for any DS games though (
https://www.dwedit.org/dwedit_board/viewtopic.php?id=480 is one for the Wario Ware GBA as well as Advance Wars 1 and 2) much less a proper analysis.
Haven't measured things in a while and I don't think we ever did a proper shootout since GBA slot carts still represented a viable method (some GBA carts are less than stock, others more, and most won't do sleep mode that well), and most of those were idling on title screen (in my experience often quite the power hungry aspect -- they often have complicated animations and unlike consoles are not really designed to sit there all day on them) between flash carts rather than playing with multimeter.