If you are biologically related, you will share a lot, but not all matches. For instance, using FTDNA's Not in Common With filter, my brother has 23 page of matches that do not reach FTDNA's minimum threshold of matching segments to be considered related to me.
In fact, he has one match in particular that matches my mother, but not me. That match has a brother that matches all of us, and who was actually in my family tree as a known cousin before I had DNA testing done.
Ex: Julie and George are full siblings and are my mom's known 2nd cousins. Julie matches my brother and my mom, but doesn't match me. George matches all of us. My mother simply didn't pass the DNA she shares with Julie to me, but she passed it along to my brother.
Conversely, if you and your brother are not biologically related, it is still possible for you to share matches, but it would be likely those matches would show as low confidence distant cousins with very small shared DNA segments and are likely Identical by State ("IBS"). IBS is a term used to describe DNA segments which match purely by coincidence. In contrast two people who are Identical by Descent ("IBD") have matching segments that can be attributed to a shared common ancestor (ISOGG definition). To illustrate this, my ex-husband and I have lots of common matches, but we do not match each other. However, our ethnic background is similar (Northern European), so it is no surprise that we would have common matches.
If you and your brother are full siblings, testing both of you will help you find more relatives than just testing yourself. And if you have a parent you can test, even better! I am trying to locate my dad's birth family, so I know if someone matches my brother, but doesn't match me or my mom, they are still a match to my dad's side. Most importantly, you'll need to get your results over to FTDNA or GEDMatch (both would be best) so you can use the chromosome browsers to determine what chromosome you match on, the location, the length and the total amount of shared segments.