I would not expect any significant similarity.
Centipede venom is completely different in effect and composition than tarantula venoms. Scolopendra centipedes ( such as S. heros ) are known to have cytotoxic compounds which can cause dermonecrosis--unlike any known tarantula. They also affect the nervous system in different ways than most tarantulas, causing an inordinate amount of pain. Whereas many tarantula venoms cause numbness and involuntary contractions of the muscles, centipede venom seems to affect humans primarily by stimulating pain receptors.
Tarantula venom is hypoallergenic only because the toxins are composed of peptides, and not proteins. Peptides are a smaller molecule that are much harder for the immune system to detect and therefore react to. Centipede venom, however, is a combination of peptides and proteins, so that there are compounds in the venom which it would be possible to become allergic to. It is unlikely that you are already allergic, as there is no reason to believe you have been exposed to the compound. Usually, the first bite "sensitizes" you to the venom, and each successive bite provokes a worse, and worse immune reaction. However, it is still possible to have a reaction on the first bite. Don't count on being allergy-proofed with centipede venom.
Allergy generally isn't the concern when dealing with Scolopendrid venom, as the stuff is plenty bad enough without any allergies. Just read the Scolopendra subspinipes thread in the Bite Reports forum.