Furret is the better HM Slave of the two because it can learn three HM moves over Raticate's two. Both can learn Cut and Strength, however Furret can learn Surf in addition to this.
Thing is, Surf is a good attack and it is very likely you'll have a Water type on your team able to use this. If this is so, you should go with Raticate (or go with neither because there are better Pokemon that can learn Strength and you vcan probably give something else Cut) because it is able to make better use of Strength as an actual attack. If you have Feraligatr as your starter, because of the fact that it uses Waterfall better than Surf, you'll want to use Furret, due to you not wanting to waste a moveslot on Feraligatr for Surf.
Try to consider other Pokemon though, these two aren't able to learn too many HMs and are not a powerful part of the team. A Sandslash would make an excellent HM Slave, seeing as it ccan learn Cut, Strength, Rock Smash, and Rock Climb. Nidoking/queen are also great HM slaves, especially if you have Feraligatr on your team. They can learn Cut, Surf, Strength, Whirlpool, Rock Smash, and Rock Climb.