All oil absorbing papers reduce shine--they're not meant to remove all the oil off your face, and you don't want it to because you still need natural oils on your face to protect your skin.
Whether it takes off your makeup depends on how you apply it, not the sheet itself: Gently blot (press) the sheet on your face to remove excess oil. Do not rub it and wipe it all over your face because it will spread the oils (and smudge your makeup in the process, if you have any on)--the sheet can only absorb so much.
I've used all of these products, and they work about the same, with the exception of the blotting papers that contain powders. I would avoid those because, one, they tend to be more expensive and, two, they tend to make you look a bit cakey since you're patting the powders on with a sheet, and not using a brush to blend them in. Personally, I don't believe in a "better" brand when it comes to these things because I don't notice the difference with the brands that glorify their sheets with certain extracts and whatnot. Since I have ridiculously shine-tastic skin and go through like 3 sheets an hour, I tend to go for quantity and not "quality."
If you don't want to spend money on blotting papers, toilet cover sheets and Starbucks napkins work just as well.
e.l.f. Essential Shine Eraser
+50 sheets for $1
-packaging is an eyesore
Daiso Japan Oil Blotting Papers
+various packs, various designs, various amounts from 100-300 sheets for only $1.50
Palladio Oil Absorbing Rice Paper Tissues
+not tested on animals
-$3.99 for 40 sheets
-the shine controlling powder looks a bit unnatural (they come in 3 different shades: Translucent, Warm Beige, and Natural); it can make your skin look cakey, especially if you already have makeup on
Zon Cosmedix 24/7 Oil Control Blotting Tissues
+non-comedogenic shine controlling powder
+not animal tested
-65 sheets for $4.99
Earth Therapeutics Oil Blotting Rice Papers
-80 sheets for $5.00
Clean & Clear Oil Absorbing Sheets
-$5.99 for 50 sheets
-sheets are a bright blue that turn into a deeper blue once oil is absorbed (very conspicuous for those of you who are self conscious about your oils)
Boscia Green Tea Blotting Linens
-100 sheets for $10.00
Shiseido Pureness Oil-Control Blotting Paper
+the shine controlling powder is very light and silky, blends well
-$18 for 100 sheets
-powder can make you look a bit cakey after several applications during the day