Good question and I'd really like to know the answers with more certainty. I'm with the camps that say (1) perception doesn't always agree with reality; (2) tires and wheels make a big difference; (3) the engine varies from day to day; (4) weather matters.
All that being said, here are my takes. First, those are curious tire choices. The rear on the Fuji is both wider and TG-belted compared to the Raleigh. Both those features make it heavier. Some here argue that width doesn't matter, but width adds weight and weight does matter. Every time you slow and re-accelerate you feel the weight and you take a bit longer to get back up to speed. Some also argue that tire pressure can be too high, which I disagree with but nobody listens to me.
Turn your handlebar with the bike stationary and the pressure high, then drop the pressure and repeat. You'll feel the increase in lateral resistance. I would think that matters in a corner, but maybe others disagree. Experiments supposedly say that rolling resistance on a real road can increase with pressure, but I question whether that conclusion applies just to straight ahead rolling and certain road surfaces. I rarely ride in a straight line or at a constant speed, so these factors would seem to matter to me. Anyway, why not go with 28mm (1 1/8") or even 25mm for both wheels, and if you want TG protection then why not both wheels? Something to consider the next time you have to invest in tires.
I have one bike which always feels sluggish, even when it wore decent tires and lighter rims. I don't know if it really is sluggish or just feels that way. Still, feel matters, but since I'm not racing a clock the actual speed doesn't. Since the bike its redeeming qualities I still ride it sometimes. I have two bikes which feel very fast and I believe they are. They certainly feel effortless to ride even if they aren't faster. I suspect geometry and wheels/tires are the key factors.