Road bike will be quicker, even than a slicked up mtb. My mate usually destroys me when we are on a MTB, when however he puts 1" slicks on his MTB and I take my road bike not only am I quicker on climbs (which normally never happens) also on flat when I put the big ring on he just doesn't have a gear low enough.
18-20mph average on a flat road without any traffic lights etc is doable on a road bike (for me, plenty of quicker guys), but You would have to be reasonably fit to maintain it on a longer ride. I can get about 28km/h (18mph) on a 90km ride but I spoke to epo-aholic from this very forum and he can average 33km/h (20-21mph) over 100km. That is quick. Also pretty much hard to do with all start-stop traffic etc. But if You're planning on taking it easy, You had a 22km/h average on a mtb than I would say 26km/h taking it easy on the road bike will be easy peasy. Different position will also help with head wind, just get on the drops and go.
Road bike is fun and I ride mine more often than my mtb, also saves the wear on my mtb, no forks/shocks to service, put on a new chain every now and then, pads and that's about it. It was supposed to be my commuter only but I got hooked up kept on upgrading to a nicer bike.
[edit] what he ^^^ said it's very hard to keep it easy on the road bike, it's sooo easy to get it up to speed etc. Every time I'm planning to take it easy it ends up with me trying to see how quick I can get to work on my short commute 🙂 [edit]