The autograph book is easier to carry, but I like the mat we had signed too. I will tell you that characters will take more of an interest if you have something for them to sign that you made yourself instead of the store-bought autograph books. A few years ago our DS was into Indiana Jones, so I created an autograph book with Indy on the cover. We stayed after the show and met Jones. He immediately knew my son was a big fan and began asking him questions. My son ended up with the gloves Indy was wearing!
The look on his face was priceless! One former cast member suggested a small to medium sketch pad because it has more space and it's easier for them to sign. Also, the larger the pen the easier it is for most characters to sign. I always take a Sharpie Flip Chart Marker (I'm a ECE teacher!) and it works well. 
Thanks this is a great idea alsoI don't know the age of your kids, but for our first trip- our kids were 2 and 5. We only got autographs at the dinners (we did 2). I did not want to lug a book and pen around the parks. . so what we did was we got story books with the characters we had dinner with in it- and had them sign them on a page in the book. For instance, we did park 1900 fare with Cinderella and crew. I bought a Golden book of the cinderella story- and had all the characters sign it. to this day- when we read it and my daughter sees the signatures she Immediately talks about our trip! I did the same thing for Mickey's dinner. . We will go again this fall and I have booked cinderella's castle and hollywood and vine with the Disney Jr characters. I plan to do the exact same thing. I love that these books will have significance their entire life
