The NEMA NU-2 standard describes a protocol for measurement of scatter fraction (SF) using an axially-aligned line source, offset at 45 mm from the central axis, in a cylindrical polyethylene phantom. In this work, which is an extension of our preliminary results previuosly published in the Proceedings of IEEE NSS/MIC 2018 [1], we aim to evaluate the performance of the NEMA NU-2 SF protocol in a Siemens Biograph mCT PET/CT whole-body scanner and a long axial field-of-view (LAFOV) total-body PET scanner to determine whether modifications to the NEMA NU-2 SF protocol are needed for the characterisation of scatter in such scanners. In addition, we evaluate the impact of patient body mass index (BMI) on SF in a LAFOV scanner. The Siemens Biograph mCT and a typical LAFOV PET scanner were modelled in GATE. Monte Carlo simulations were performed to validate the mCT scanner model against published experimental results. SF was estimated using a modified NEMA NU-2 protocol with variable radial offsets on both scanners and compared to ground truth SF measurements obtained with a uniform-activity cylindrical phantom. Correlation between BMI and SF in the LAFOV scanner was evaluated by simulating anthropomorphic phantoms with different BMIs and realistic 18F-FDG distributions, together with uniformly-filled 200 cm long cylindrical phantoms with equivalent effective diameters. The optimal offset was found to be either 60 mm or 80 mm, depending on the chosen optimality metric. We conclude that modifications to NEMA NU-2 are required for accurate SF characterisation in whole-body and LAFOV scanners. Finally, SF in anthropomorphic phantoms with realistic tissue concentrations of 18F-FDG was found to be strongly correlated with SF in an equivalent-volume cylindrical phantom for the LAFOV PET scanner; BMI was also found to strongly positively correlate with the SF.