Both reviews, and power specs for the A100 suggest that it should be able to drive the 600 ohm DT880 with no issues.
I think what you are hearing is the difference between the very neutral DT880 and the quite coloured MS1. For reference, I have owned both. The MS1 are very mid forward (like a lot of Grados), with quite forward upper mids, and more mid bass than sub-bass. The DT880 are very flat across the entire spectrum, with a bit of a boost in the treble. The MS1 also has a very narrow soundstage - which puts you on stage with the musicians. The DT880 has a wider and deeper stage which will sit you back a little.
So the sound differences you are hearing are normal. If you try listening to the DT880 (and only the DT880) for 3 days - then go back to your MS1, you may notice some changes in your original impressions (because your ears/brain will have adjusted to the DT880 sound).
As far as sibilance goes - what are you listening to (genre/band)? I've never had an issue with sibilance with my Beyers unless it has been present in the music already. Some headphones will gloss over this (not as resolving). The Beyers will show you what is present.
Burn in isn't going to change much - unless you're talking about brain burn-in (see my comment above). A lot of people do like the DT880 with tubes (myself included) - this comes down to individual preferences.
I'd give it 3 days with the Beyers (listening to no other cans), then go back and compare with your MS1. If you are still not impressed, then you bought the wrong headphone for your preferences.