I think the weights for the newer X35 13x11" are 590 grams with coil cover, and the older 13x11 at 662 with coil cover.
I can't compare between the newer coils due to weight and performance differences, though for me I found that I used the 11" and 9" coils much more often than the original 13x11". The 13x11" was purchased more for areas where iron/junk was at a minimum, for longer hunts the 11" and 9" are a lot less fatiguing with regards the weight, and are more well balanced on the shaft due to where the lower shaft is mounted on the coil.
The 11" coil despite being heavier than the 9" coil, doesn't really feel that much heavier in the real world. Swap over to the 13x11 and the weight is definitely much more noticeable.
I think many people have problems with the older coil due to having the lower shaft over extended and swinging it too far away from their body, sometimes that can't be helped, especially if you are a tall person. I am not the tallest person in the world, so I can get away with swinging the larger coil much closer to my feet, resulting in less fatigue. I am also not a big user of the arm cuff strap when using the smaller coils, though you will find it is a necessity running the larger coil due to being more nose heavy.
Just have to weigh up on what areas you are more likely to detect, if on older sites where iron is prevalent, there is no getting past the unmasking ability of physically smaller coils - same for junky areas around ovals/parks. For me that means the 11" coil has the best of both worlds - more coverage whilst still retaining good unmasking ability.
If you are detecting open paddocks, large parks with minimal junk, or at the beach, then the coverage of the 13x11" may prove to be of an advantage, especially if you like to grid to recover as many targets as possible.