Cool, I didn't know Teledyne LeCroy rebadged the SDS1104X-E.
Some other differences:
T3DSO1104 claims to have higher bandwidth probes - 300 MHz
SDS1104X-E comes with 100 MHz probes.
Teledyne LeCroy sticker on the top front corner - can I get ones of these for my Siglent
Marketing screenshots for T3DSO1104 show no logo on the display (where Siglent would have a Siglent logo).
Not 100% sure, but Teledyne LeCroy does not seem to have easy access to download firmware for the T3DSO1104. Siglent has anonymous download of firmware from their website.
For example new firmware just came out for the SDS1104X-E and I don't see where to get new firmware for the T3DSO1104 from the teledynelecroy.com website. I might be looking in the wrong place? Perhaps you need to contact their support for it. But I don't see announcements for new firmware either so how are you supposed to find out about them - unless you follow Siglent updates as well?
Probably different locations for distributors/repairers - in case you need support.
EDIT 20200318:
Someone pointed out to me that since my post above, Teledyne LeCroy now has the current firmware available for anonymous download from their website.