What each method actually is
Sublimation dyes your entire design, colours, patterns, numbers, sponsors, directly into polyester fabric using heat. The design becomes part of the material. Embroidery stitches thread into the garment: raised, textured, premium to the touch, but limited to smaller areas like crests and initials.
They're not really rivals: most premium teamwear uses sublimation for the garment design and embroidery for crests on outerwear.
Durability and weight
Sublimated prints cannot crack, peel or fade, the ink is inside the fibre, so the design outlives the shirt. Embroidery is equally durable but adds weight and stiffness; a fully-embroidered match shirt would be unwearable, which is why embroidery lives on tracksuits, hoodies and polos.
Heat-pressed vinyl (the third option you didn't ask about) is the one that cracks in the wash, it's what sublimation replaced.
Cost and design freedom
Sublimation's superpower: complexity is free. A shirt with five sponsor logos, a gradient and 20 player names costs the same as a plain one. Embroidery prices per stitch-count, so a large complex crest can cost more than the garment.
Searches for embroidered football shirts are rising fast (fashion-led, retro terrace culture), and we do offer embroidered crests on sublimated shirts for clubs that want the raised-badge feel with modern fabric.
Our recommendation
Match kit: sublimated, always, weight, breathability and printed numbers decide it. Training wear and club leisure: sublimated body + embroidered crest is the premium combination. Committee polos and gilets: embroidery earns its keep. Ask for both in your mockup and compare.