I'm not entirely sure what you mean. To formalize what "hard" and "easy" mean it would take forever. But what I mean is the verifier's computer just isn't strong enough to check whether the graphs are isomorphic or not.
Here are two graphs I just made in Python. Both vertices list are 1 through 100, both have 50 edges.
Graph 1
E = [[61, 64], [95, 22], [50, 29], [14, 32], [28, 56], [41, 77], [41, 42], [80, 82], [26, 4], [57, 99], [12, 17], [87, 69], [93, 13], [20, 4], [76, 14], [4, 94], [53, 98], [77, 74], [71, 28], [9, 90], [58, 60], [49, 59], [24, 54], [19, 12], [44, 34], [2, 32], [1, 54], [77, 12], [37, 37], [17, 86], [16, 92], [65, 52], [40, 30], [37, 71], [51, 43], [14, 9], [13, 67], [59, 31], [14, 75], [33, 83], [16, 77], [3, 33], [94, 72], [70, 22], [96, 87], [86, 78], [46, 36], [53, 33], [98, 4], [71, 22]]
Graph 2
E = [[40, 25], [80, 38], [30, 69], [93, 59], [1, 50], [90, 85], [14, 20], [68, 27], [7, 55], [61, 74], [37, 80], [33, 64], [86, 49], [83, 32], [37, 13], [4, 75], [87, 72], [4, 24], [50, 42], [46, 92], [50, 80], [67, 20], [20, 63], [63, 71], [10, 87], [44, 71], [30, 89], [29, 73], [82, 47], [88, 5], [53, 6], [82, 56], [51, 51], [54, 32], [53, 67], [69, 75], [33, 8], [55, 100], [53, 16], [53, 19], [89, 43], [4, 96], [9, 58], [21, 2], [66, 19], [51, 65], [80, 87], [46, 17], [24, 58], [69, 1]]
It's not really that easy to check if there's some way to relabel the vertices that would make all these edges to match up.k