No rule of thumb or guesstimates?
I said above that one company reckoned a 90x405mm glulam was required based on 6.4m span, 6.0m unsupported. I'd happy entertain educated guesses from people with some experience what approximate RSJ might be equivalent.
If I can get my SE to verify, you could win bragging rights
You told the company who gave you that approximate size the span of the beam, but did you tell them the width of roof the beam was supporting? - obviously that has a direct bearing on the load the beam is to carry. Most SEs will not sit down and work out a size of glulam beam because it's not cost-effective time-wise - you generally go off manufacturer's tables for commonly-produced sizes, but they need to know the load it is carrying. (If you want to see the figures, Google 'Structural Timber Design' by Abdy Kermani and you'll see why most SEs won't be bothered).
Design of steel beams is an 'iterative' process, in that you choose a section you think will work, and then check it for stress, buckling and deflection until you get the smallest-size section which satisfies all three. I'll stick my neck out and, on the sparse info you have given, would say one of the 254 x 146 beams might work? or possibly a slightly bigger one, or smaller one - who knows?