Both are good amps, but by all accounts very different. The Gilmore Lite (bearing in mind I am going off what I have heard about it) probably sounds cleaner and more detailed than the Perreaux, the Perreaux going for a more forgiving, warmer sound. Neither amp is probably better than the other, and it will come down to personal taste.
Slotting the SXH1 in your system will likely make things a bit warmer, but really it is only going to be a side step, is that what you want?
If price was an indicator then the Perreaux should outperform the Gilmore Lite...
However, it certainly is no accurate indicator of performance IMO, and add to that, the difference between amps is usually pretty subtle as well, as it should be if the amps are doing their jobs properly (that is, reproducing exactly what it receives from the source without adding or subtracting anything that wasnt there in the first place).
I don't have much experience with tubes, in fact my only experience was a very brief go with my Fender strat and some old Fender tube amp... so this is more of a question than a statement. Experts will correct me in how I'm voicing what I hear, if I'm wrong.
The sxh-1 to me kind of mimics a tube sound while still being solid state. It also does alright with my ms-1's, but my setup mostly involves Senns. It's just that it's not illegal to pick up the Grados when you need them. But it does seem that if you're more of a Grado person than a Senn person, that the Glimore would top the list. That is, if public opinion here is anything to go by.
edit - Not to harp on the pricing issue, but I'd like to once again point out that the Perreaux may not be so overly priced - depending on where in the world you live. Not everyone is under the control of that crappy US distributor.