Do they give the same boost or is one higher than the other? I know the hatching purposes vary a bit with wave producing an azurill and sea producing mantyke egg but is that it?
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The Sea Incense was introduced in Gen 3, and until Gen 4, it only increased the power of Water type moves by 5%. In Gen 4, this was boosted to 20%. The Wave Incense was also introduced in Gen 4, and has always boosted the power of Water type moves by 20%.
The only other difference is that the Sea Incense allows Marill or Azumarill to have Azurill eggs, and the Wave Incense allows Mantine to have Mantyke eggs.
Sources:Sea Incense,Wave Incense
For battle Sea Incense boost water type moves by 20%, while Wave Incense just boost all water type moves.
For breeding, Sea Incense causes Marill and Azumarill to produce an Azurill Egg while at the Pokémon Day Care, while Wave Incense causes Mantine to produce a Mantyke Egg while at the Pokémon Day Care.
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