I would consider almost every other Premier League club except for Bournemouth, Huddersfield and maybe Watford and Brighton to be "bigger" than Burnley, as well as most Championship clubs and even some League One clubs (e.g. Sunderland).
However, given how well he fits in at Burnley and their success over the last few years I don't think it would be wise for him to move to another club battling for mid-table, unless of course Burnley get relegated. He's already at a mid-table team that did finish 7th last year and played (badly) in this year's Europa League.