Simulation discrepancy in Qucs with 2N3904 transistor
The hFE of the 2N3904 is typically around 40-50 at 110mA Ic and Vce = 1V, according to this datasheet and this datasheet.  

Your Qucs simulation shows 2.2mA base current with Vce = 1V and Ic = 110mA, so hFE is about 50, which does not seem unreasonable. 

The LTSpice simulation seems a bit more dubious, for that part number, at least based on the above datasheets. I believe you're probably using the Philips model in LTspice, which seems to have an unusually high hFE at 110mA for a crappy 2N3904. The 2N3904_Cordell model has lower hFE, at high current anyway. You're really out at the edge of where people would use a 2N3904 anyway, so I'm not sure it's even that useful a comparison. Try at 5 or 10mA Ic and see what the differences are. 

You should be able to compare the model parameters to see what the differences are. You're changing two things at once (model and simulator) so you're not really comparing simulators. 

I believe that both are based on Berkeley SPICE 3.x so the simulation results should be similar, all other things being equal (and there are many options with each).