Climate change mitigation requires radical reductions of GHG emissions. The potential of different strategies to reduce GHGs is subject to fierce debate and investigation, the assessment of strategies requiring a technology-rich scenario approach. Technology-rich Integrated Assessment Models (IAMs) contribute to prominent science-policy interfaces such as the IPCC but have an important shortcoming: although material production accounts for ~1/4th of global GHG emissions, most IAMs ignore potential interventions in material life cycles as GHG mitigation option, which makes these assessments incomplete and neglects the contribution materials can make to reduce impacts. Recent advances in integrating major material flows into IAMs try to tackle this gap. However, the accurate quantification of material cycles is a challenge even in the scientific field primarily occupied with this task, Industrial Ecology, which merits the validation of indicators across methods. Here we compared the material stock-flow indicators used in the IAM MESSAGEix, with recent results from Industrial Ecology and explained emerging differences by examining underlying data, for example activity (e.g., m² floor area) and material intensity (e.g., kg cement / m² floor area). For the comparison we obtained semi-independent data from (a) top-down, economy-wide Material Flow Analysis, as well as bottom-up, stock-driven data from (b) spatially explicit material stock, and (c) sectoral statistics-based stock-flow modelling. The target scope was the data-rich case study North America (USA & Canada) for the base year ~2015 and the sectors residential buildings, non-residential buildings and power (including preliminary data on roads and motor vehicles). For overlapping system definitions, total material stocks varied by a factor of up to three among studies, stocks by material by up to fourteen, over the three sectors power, residential and non-residential buildings. For stock-driven studies, the varying stock levels could be explained by differing activity levels (up to factor 2) and/or material intensities (up to factor 33). For the top-down, inflow-driven study, the cumulative consumption of bricks for 1870-2017 and estimated from statistics was <60% of a bottom-up material stock estimate, potentially indicating underestimation in respective statistics. The large differences of material stock estimates call for improved data and data reconciliation of activity levels, material intensities, material consumption and its end-use allocation, as well deeper cross-methods analysis. Data differences might emerge from: using activity data assembled for purposes other than material cycle modelling and resulting system boundary differences among studies; few available case studies on building material intensities which through intransparent documentation, heterogenous data processing and selectivity can lead to variation of applied intensities; the challenge to represent heterogeneity of technologies while being comprehensive in scope; and non-market material extraction not finding its way into statistics (e.g. for bricks). For the momentary modelling of climate change mitigation through material efficiency, our results stress the need to explicitly address uncertainty through scenario and sensitivity analysis in order to ensure robustness of conclusions.