As above- my dts are in y6. They are similar- not quite the same- in ability. DT2 just edges it. The main difference is that DT2 is super driven and confident, so much so that sometimes- alright, all the time- it seems as if DT2 has all the confidence, DT1 all the self doubt. The two of them could both do with sharing it out a bit
they're non ID, like yours- and DT2 is the tallest and the thinnest (alas, for all my hard work at this end, this matters to Y6 girls) and also the most popular- though I feel a lot of this is because she has a kind of 'if you don't like it, fuck off' attitude- she's not rude exactly, but she doesn't ingratiate herself much- she's got other things to think about. I'd say that she's considered cool rather than nice (this also counts with Y6 girls)
They've been in different classes all the time they've been in primary- though they're streamed for maths, so in the same group.
The problem I've found in y6 is that, because of SATS, any differences between pupils are very marked- they've all been very aware of their SATs grades since the first term of the year. Each time DT1 has had grade she'd ordinarily be pretty pleased with, DT2 has got one notch (sometimes two) better. In addition, DT2 has been picked for everything- sports things, school council, now the Y6 play, where she has one of the biggest parts and DT1 has one that's respectable, but not great.
We have had untold tears over this- in secret. DT1 has been very nice and congratulatory to DT2's face but fallen to pieces with me 
I've had to email the teachers- in secret- explaining the situation, asking them to not add to DT2's role- (I know, how awful to find yourself in the position of asking teachers NOT to push your child- but I fear long term damage to their relationship otherwise)- they've been very helpful, and given DT1 extra music stuff to do as part of the play (both girls do music but- of course
- DT2 is a grade and a half ahead)
I agree with pps about other activities- this is working for us, touch wood- it's early days yet. Also I would say don't move DT2, keep him in the school where he's happy- is there a sympathetic teacher you could talk to? It's really helped us.
You have my sympathies; this is such a difficult issue. We have spent 11 years resolutely trying to ensure everything's fair and Not Comparing- but as you say, other people inevitably do- teachers, relatives, friends (DT1 was recently asked by a friend 'what's it like to be twins with the cleverest girl in the school?')