It is certainly true that Tyris' main benefit in arcade is her stronger magic. However, there are also differences in special attacks/hitboxes. Tyris has a spinning backwards attack for her special. This lends itself better to combos than Gilius' rolling backwards attack. Her hitbox also feels smaller (although I cannot prove it). Ax has the same spinning backwards attack as Tyris. His running attack (shoulder barge) has a hitbox that makes it less useful, although is has the unique ability of being able to hit enemies attacking from behind (if you charge away from an enemy that is about to run+charge you, the enemy will be hit and fall in the direction of your charge). Ax's hitbox feels like it's the biggest (again I cannot confirm). Gilius has a rolling backwards attack. It has different benefits to the spinning backwards attack. It cannot be used as easily in combos due to it's range, but this means it can be used to hit enemies who are off screen at a greater range than any other character. Overall the easier combos with Tyris' spinning attack make her the best choice for me. Most of the time it's possible to keep the enemies on screen which makes Gilius' rolling attack less useful, whereas the frames saved not having to re-position to chain a spinning attack saves more time.