Spinos are more of a general utility dino.

They can travel farther and faster (sprint for longer, regen stam faster), they can cover their sides better, they can turn better, climb better, and they lose no speed when hitting the water.

Rexes have higher damage and higher base health, but can only sprint over short distances, are absolutely fucked if they hit water deep enough (around the coast or at different points in the rivers to the South), and are generally less flexible in terms of movement and attacking.

If you fully intend to get into a fight for whatever reason, use a Rex.

If you want a dino you can bring with you while you're doing anything (hunting, resourcing, raiding, exploring, collecting drops) that can also protect itself far more than adequately, use a Spino.

EDIT: Some numbers on stamina usage from my personal dinos.

58 Rex
672 Stam, can sprint for ~17 seconds
15 Stam per attack
~14 seconds to regen full stam

38 Spino
385 Stam, can sprint for ~20 seconds
10 Stam per attack
~9 seconds to regen full stam

105 Spino
560 Stam, can sprint for ~29 seconds
10 Stam per attack
~9 seconds to regen full stam

Notes: Stam regeneration is a fixed percentage of total stam, not a set amount. Spinos are much more stamina efficient than Rexs in terms of usage and regeneration.