Sorry to disappoint you, Newtowheels, but a new bike won't make you noticeably faster. That's true for commuting and that's also true for racing... except that a 2-second difference often makes the difference between a first place and 50th place in the standings.
I don't know your bike model, but there are things you might be able to do to improve your ride:
– New tires. If you have knobby or wide tires, replace them with narrower high-pressure slicks. Something like 700x32 or 700x28 (narrower if you are light), or I think 27"x1 1/8 OR 1 1/4". Tires without sculptures run faster and are silent.
– Modifying gear ratios with a new freewheel if necessary.
As for buying a new bike, you might go for a touring or sports-touring bike (curved handlebars), or a good hybrid (straight bars). What would you get?
– Indexed shifting and shifters on the handlebars, which means you won't be looking for your shifters nor for the exact gear. Adjustment is more finicky, though.
– More gears, with a 9-speed rear wheel as opposed to the 5 or 6 speeds you currently have. So you will be able to fine-tune your gearing and this will provide you a small speed increase... and a great improvement in comfort.
– Better hubs. The hubs you have might not be well sealed, which means they are OK as long as they are regularly maintained. Newer hubs, especially the Shimano mountain series (LX, XT...) have seals that are very efficient at keeping the grit outside the hub.
– More rigid bike. Frames built 20-30 years ago were more flexible than modern ones. That's great if you travel without a significant load on a bumpy road, but if you start piling stuff on the rear rack, the bike will eventually feel like a wet noodle. So if you commute with full panniers, a new bike will be more rigid.
And then, you get all the subjective aspects:
– Better positioning: assuming the other one doesn't suit you perfectly.
– Comfort, which depends on bike geometry and tubing selection. Hard to be more specific, so you'll have to enquire.
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The "nice-bike" effect.