My take is if this is your first time in BKK, the river views from millennium rooms and lounge are wonderful. It's also slightly less congested than sukhumvit, but harder to get in. Conrad is wonderful, great service, but it's more like a business hotel.
Overall, for a romantic gateway, millennium is probably better. More seasoned visitors who like the chaos of the city (me), would probably pick Conrad, or flip a coin between millennium and sukhumvit if Conrad is too expensive ---which is the case more often than the others.