Wife and I have been going back and forth about removing two very large
trees from our front yard.
Tree guys that have come out have called them swamp maples or silver
maples??? Not sure what the difference is.

Never heard of a swamp maple. A silver maple is a fast growing trashy tree.
But a big one is still worthwhile, as long as it is not growing over your
house; the branchs break pretty easily.

A lawn guy that came out said these trees have shallow roots and take
nutrients away from the grass.
We have a small front lawn, about 80' x 30' with these two trees on each
end.
I would like to remove both trees and have the stumps ground down. Tree
guy
said he would grind 6" or so below ground level and we could fill it over
with soil. I asked about the stump rotting and he said it wouldn't happen
for a hundred years ???

More like 20 years.

I'm guessing the underground stump will rot and cause a depression that
will
have to be refilled over time???

Yeh, I found a few that the former owner did; it can be surprising when the
ground just caves in.

Also He said he would leave allot of the wood in 4' length and I could cut
it down and use it in my wood/coal stove.
is "swamp maple" good to burn? He said it was a hard wood. It would be
green
so I guess I'd have to wait until next year to burn it. We live in
Massachusetts...

Silver maple is mediocre fuel; probably better for a fireplace than a wood
stove; though for free I suppose it is fine. (see soft maple)
http://www.mb-soft.com/juca/print/firewood.html

$1800 to cut both trees, grind two stumps (plus two smaller stumps in back
yard) Haul away the big trunks and grind up the smaller branches. and
leave
me wood cut and burn. Not sure what a cord of wood costs but it would help
defray the costs of the cutting!!!

The price doesn't sound bad.

I'm also going to ask if they can leave me a section of the large tree cut
about 3 feet long. My dad had a section of stump like that when I was a
lad
and we used it as a work surface in the work shop to pound on...

I think the trees are overgrown. they are growing into the wires in the
street (power co wont trim them despite repeated calls)
every time we get a storm a dozen branches fall in the yard. I would
eventually plant 1 new tree and start over.

My wife is concerned about the loss of shade on the house.. I think having
the trees is more of a problem as our old roof (replaced 2 years ago) had
moss growing all over it because of the trees hanging over it.

It will certainly alter the look of the yard and may look odd at first but
I
think they are to large for the lot and after a couple of years we would
never miss them???

I would be interested in any thoughts on this matter, Cut them down or
save
the trees????

Personally I like big trees, but you live there.