Currently staying here this week. My last couple of stays in Moscow have been at the Sheraton Palace, so I'm able to compare the two.
If you are staying for business, the Sheraton is more comfortable, especially on the club level. I know the 3rd floor hasn't been updated, so if you can swing a higher floor, you'll be happier.
As for the Hotel National, it needs some updating. The lobby area is straight from the 60's, which would be cool (I like the look of that era generally) if it didn't feel so worn. They probably need to lose the wall of pictures of dignitaries on the 2nd floor -- a hotel of this class shouldn't have to derive prestige from people who stay there.
Also, after using the gym at the Sheraton, the Hotel National gym area probably needs a bit more space and a more spa-like feel vs. the late-80's feel of the space. Would be great to have ellipticals too. There is a pool, which the Sheraton doesn't have.
Food on the buffet was generally the same as the Sheraton.
As for convenience, the metro is closer to the Hotel National vs. 5-10 minute walk from the Sheraton. And it is kind of cool to walk out of the hotel and see Red Square and the Kremlin. And, unlike the above post, the concierge has generally been helpful.
If I had a choice, I'd stick with the Sheraton, but the prices have basically doubled in the last month or so, so it's difficult to justify the additional cost above the rate I'm getting at the Hotel National.