Indeed, the Hawk is a rather poor defender, and although its opening / middle-game value is more than that of a Rook, it loses against some pieces a Rook can draw against. E.g. Chancellor vs Rook is a draw in most cases, but the Hawk generally loses against Chancellor.
A Spider beats a Hawk in 98.7% of all positions, when it has the move. This is actually a bit low for a generally won end-game, but there are probably a fair number of start positions where the Hawk, with its 3 jump, forks Spider and King from a safe distance.
The Spider wins as it can mate alone. In such endings, it's superior to the Queen.
1. Hd6+ Ke6 2. Hd3 Sf4
3. Ha3 Se3+ 4. Kb2 Sc4+
The Hawk is lost and the mate will follow easily. Be careful of stalemates !
5. Kc3 Sxa3+ 6. Kd4 Kd6 7. Ke4 Sc2+ 8. Kf5 Se2 9. Kf6 Se4+ 10. Kf7 Sg4 11. Kg7 Ke6 12. Kh7 Kf6 13. Kg8 Sg6 mate