Reddixie,
Kind of hard to compare, it's not even apples and oranges. More like apples and potatoes. But having stayed in both, I'll try...
When are you going? And what do you want to accomplish? I can't normally tell the difference between a good mattress and a rock, but DW says they were both "ok." She prefers soft mattresses. I guess that would mean they aren't hard. Hope that's a good thing.
As for how they compare: They are both older motels. Both clean, both with wear, both get a different rating from me depending on how much they charge me. Note: my comparison will assume a poolside deluxe at HJME (we are talking Maingate East?). That's the only room I've ever used at HJ. You get better location, a bigger room, and a microwave and refrigerator. The size of the rooms is similar, but I'd put the Grovesnor at a bit bigger. In short, they're both basic old but clean hotel rooms. One main differnece: Grovesnor has internal corridors. I consider this a blessing, rather than the HJ type where your corridor is outside, usually in front of the pool or 192.
The differences: location. HJME for an offsite is a good hotel, for a good price, for a good location. It's pools are nice (they have two, I'd suggest spending time at the one WITHOUT the bar, it's always less crowded). Lot's of convenience stuff (restaurants, stores) within a two minute walk of your room.
But the location doesn't compare with Grovesnor. If you're spending a lot of time in the Epcot area, and especially DTD, then you can't beat Gorvesnor. It's perhaps the closest hotel to DTD (a ten minute walk, max, to the Marketplace). Although it's theming standards aren't the same as regular Disney properites, it is somewhat themed (an old Baskervillian mansion theme, complete with a Murder Mystery Theatre). Amazingly, it seems to have less pool space than the HJME, but it's adequet.
If it was me: I haven't stayed at HJME since I discovered Priceline, because I don't mind taking pot luck when I need a low-end place, and I can get HJ quality at under thirty bucks. But I always found it a suitable hotel for what I believe was $45 a night for the deluxe room (push for that price, they will give it to you). But If I could get the Grovesnor for $69 (which I've seen for fall season) or even in the $80 range, I'd take it over HJME simply for location.
Hope that helps. Any other questions I missed?
Pat