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There are different schools of thought on that. I'm not sure if there's definitive proof either way. But here's my opinion, based on experience.
If you do the "slow and steady" thing, you may never get up to cruising speed, depending on road conditions. And cruising is where you save gas. If you're always accelerating (even lightly), you're spending more gas than if you're cruising.
You also have to consider the time component. If you accelerate briskly for a few seconds, then settle into a cruising speed, you were only wasting gas for a few seconds. If you accelerate slowly for a much longer time, the fuel is burned a lower rate (compared to brisk accel), but for a much longer time period. So the total amount of fuel used may not be much different.
I'm sure you're familiar with pulse & glide. It's a similar idea. And it's proven to work. The logistics of pulse & glide vs steady-state cruise are similar to brisk acceleration vs slow acceleration. Plus if you accelerate briskly, you can get into the P&G zone sooner.
Those are my thoughts on the subject. But if you have the time, maybe you can test it and find out!
Side note: P&G is even more effective with a diesel engine. Because diesel engines burn minuscule amounts of fuel at idle (much less than a gas engine). So maximizing idle time will pay big dividends with a diesel. This has nothing to do with your situation, but may help some of the viewers.
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