Subtext: When would the industrial revolution, with its associated inventions, have come to pass if the Roman Empire -- in an alternate timeline -- had been a more stable entity?
The Europeans were actually quite a bit more advanced than the late Romans.
The horse collar and the associated harness allowed for heavy plows and the tilling of land that had not been able to produce as much grain as previously. Farmers could plow deeper and seed the soil in a way that protected the seeds against the frost better, and land further north became more productive.
The introduction of the scythe to replace the sickle also made it possible not only to harvest more crops (it seems farmers started to use the scythe for harvesting crops towards the end of the medieval era) but also to scythe hay to keep livestock over winter much forther nort, and to keep more livestock alive. Dairy and dairy-based products become more common during this era as a result.
The horizontal loom allowed for more effective weaving and gave birth to the English-Flemish wool industry.
The invention of the windmill, to drain land, irrigate or mill allowed deeper mines, easier milling away from streams or the usage of humans or animals in a treadmill.
The introduction of optics - both for early telescopes and for glasses during this era allowed the study of astronomy and for learned men to read and work for longer.
Navigation became easier - the invention of the compass and quadrant and the introduction of larger vessels built with cravell technique (such as the carrack/nau or the caravel) and multiple masts with multiple sails all allowed more extensive trade over longer distances.
By the 14th century, rudimentary cannons had been introduced, complication fortification construction and revolutionising warfare. The stirrup and the medieval saddle had made medieval cavalry far more dangerous than its Roman counterparts ever were.
This is just a small excerpt on things in which medieval Europe was more advanced than the Roman Empire.
As for the industrial revolution, it is my experience and pet theory that the industrial revolution does not happen, or is severely retarded in places where large landowners hold the economical and political power. To them, slavery or serfdom is profitable and preferable and they have little incentive to invest in labour-saving machinery, tools or factories, thus providing neither the market nor the investment needed for an industrial revolution.