I've never actually stayed at either. This is just a general feeling from having stayed in some urban older boutique hotels. Best bet is check trip advisor I think.
One thing about trip advisor when looking at reviews. I usually only give weight to those who have several reviews(sound familiar lol).
Gladstone has good food, excellent staff, unique rooms, and is closer to spots like Electric Mud and Grand Electric. Drake has smaller rooms, great brunch and likely appeals more to the ladies that will visit you. I prefer the Gladstone.