Just for budget reasons, if they looked the exact same and the size was negligible, I'd do the .9 carat because there can be a price jump from .9 to 1 carat.
This is my personal opinion. I think the 1 carat being the ideal weight is overrated, and I would never buy a stone right at the carat break because the cost increases tremendously at that point. There is a phrase "buying shy" where you buy 0.1 carat under the major carat breaks to avoid the huge cost. The spikes where prices per carat jump are referred to as "magic numbers" or just magics in the trade. The chart I attached is outdated, but the premise remains the same. Look at the carats where the number of stones is higher. Those are the price jumps. That is also why you don't see a lot of stones that are say 1.4 carats, because the cutter can fudge the cut on that stone and make the proportions/cut lower quality to get up to 1.5 carats and get way more money per carat. Every carat (1,2,3) has a huge price jump, and every (1/2, 1.5, 2.5) has a lesser price jump, and every 1/4 in some case may see a 5-10% jump until the next 1/2 carat is hit. If I could I would try to go 0.85-0.89 carats and stay under 0.9 carats, but that is because I'm all about being frugal, and I would use that money to try to upgrade on the cut.
Magic numbers 0.25 carats, 0.33 carats, 0.5 carats, 0.7 carats, 0.9 carats, 1 carat, 1.2 carats, 1.5 carats, 2 carats, and so on.
are you color sensitive? there are many people who are ok with an I color but J for them shows too much tint from the side. What are you most comfortable with? When you look at them side by side, do you see a difference? And if someone asked you, are you comfortable saying you have a J color? (some people aren't)
What are the actual dimensions of the .9 vs. the 1ct? Are both ideal cut? Assuming both are ideal cut and the 1 carat has a larger diameter, I'd go for that, but if it's a negligible size difference (actual measurements), I might go for the .9 for the slightly higher color. A J color stone is definitely personal preference. I have an I color stone, and one of my cousins has a J color ACA from Whiteflash--her stone is much larger than mine, but in some lighting, you can see the slight body color. That wouldn't bother me for the size, but for some people, it would.