For me it would come down to a question of cost, which would be less expensive, factoring in all of the real costs (transportation included). As long as I could pick up the seed for winter rye, without making a special trip to do so, or could pick up enough eel grass, again without making special or extra trips, then probably the eel grass (if its free) would be the choice.

Ditto kimmsr's advice...but you may also want to consider that the roots to a cover crop are an additional level of ammendment. How about splitting the area and grass-mulching-turning under one side and cover-cropping-turning-under the other side...and see if you notice a difference in tilth, water-retention, productivity, etc. And, of course, report back to us on the different results [or lack of differences] BTW do you use the eelgrass for mulch in the summer? And, greedy me, I'd be tempted to green manure AND use eelgrass in a compost pile. :)
///
There is a study from the Rodeale Inst. about the need for beneficial soil fungi needing roots as a host to remain active. I couldn't find that study, but the following link might help.
...snip....WeÂve found these mycorrhizal functions provide many direct and indirect services including increased agricultural productivity, improved water-infiltration and water-holding capacity, and soil carbon sequestration
/// FOUND THE STUDY LINK
http://rodaleinstitute.org/node/441
....snip....Yet because endomycorrhizae are 'obligate symbionts'--they must have living plant roots to colonize in order to complete their life cycle--their numbers will decline under conventional agricultural monocultures, which have living crop covers fewer months of the year than organic rotations. The drop in yields typically seen after the first year of cultivation on virgin prairie or forest soils is probably attributable in part to the loss of native mycorrhizae, Douds says.
....snip...."Over-wintering cover crops. . . are very beneficial to mycorrhizal fungi,"

Here is a link that might be useful: Mycorrhiza

My gardening practices are rapidly evolving as I learn more. I owe thanks to borderbarb (thanks Barb :) for the links to the mycorrhizal information. This fall I'll be sowing a cover crop and I'll be covering the sowed bed with screened compost.

The cover crop will be for the sake of the fungi in the soil, the compost will be for the sake of the bacteria at the surface of the soil.

Getting eelgrass is a matter of driving a pickup ~1/4 mile and pitch-forking it in. I use it for garden paths, mulching plants, and a bit in compost, although my composting mostly revolves around processing fish scrap with wood shavings, chips, and such. Last fall I put down about a pickup-load per 200 sq ft, and was surprised to see most of it pretty much decomposed by now. It's easy enough to do it again this fall, but I'm worried about relying excessively on a single soil amendment.
Winter rye seed is also easy enough to get, but I wonder if it can provide as much nutrients as an 8" layer of eelgrass.

I don't know how dense a surface the eelgrass presents, but do you think you could put a thin layer of eelgrass AND then sow the rye seed? [best of both methods?]

Some of these threads should have an ENVY WARNING. Having a pickup truck, access to composting/mulching eelgrass source, fish scrap for compost pile...etc. YIKES! My envy level is soaring....better go out and count my many gardening blessings to counter-act the envy factor.

Oh, lest envy show up, let me mention soil (sand, that is) that would make any beachgoer grin, the New England spring (still waiting to break 70F, pretty much), New England fall, New England winter, New England bureaucracy that won't let me take down trees on my property, a grey squirrel every two feet, coons, watering regs, and.... need I go on?

Free fish scrap and seaweed seem to fade all of a suden, don't they?

personally
with eel grass readily available
I would plant the rye
and mulch with the eel grass that has been composting overwinter next spring when I plant.
A green manure will send roots deep into the soil
something a mulch can not do.
compost the eel grass
plant the rye
best of both worlds

That does indeed make the most sense.

Now, if I have some unfinished (eelgrass) compost come October, am I better off turning it into the soil in the fall, or leaving it in a compost pile until spring and putting it on the garden then?