Personally, it makes very little difference. If someone is quicker than you, it's because they are fitter than you.
Yeh it's nice having a best bike, but I'd not say it makes much difference in the real world. I can still set similar 'strava' times on segments whether I'm on a fully loaded fixed gear commuter with panniers or my 9kg steel bikes (yeh not super light, but not bad for steel considering there is a 2kg frame and fork penalty - 3.5kg steel vs 1.5kg carbon).
MTB's are a bit different, but it still boils down to the rider.
So a Traban 5 won't be slower than a £1k bike. Stick some quality race tyres on and the bike will feel much livlier though.