I've stayed at both in the last six months, and enjoyed both. The Regent is quite modern, and has fairly large rooms; I found the service to quite good - not FS quality, but nearly.

The Adlon is much more of traditional European "Grand Hotel". The rooms are a fair bit smaller, but quite luxurious in their own right (my deluxe room had a mini kitchen behind some sliding doors); the service was outstanding.

I'd be happy at either one, the Regent is slightly less expensive.