They are both lane bullies and have very strong laning phases. Draven's Qs make it very very easy to last hit, and do insane damage for in lane harass. He also has a very hand MS/AS increase, but you blow through mana very quickly if you use it a lot. You shouldn't ever have mana problems on draven unless you are constantly fighting. Though, unless you are really far behind, or they are trading damage amongst themselves very well, they will be forced to back because they are probably almost dead. His ult is very strong and lets you do cross map stuff and what not. I don't recommend using it to farm like you can ez's ult since it has a longer cd and your Q doesn't lower your cds. It does a lot of damage if you can lay it through a team though.
MF is my go to solo Q champion. Once you figure out how to harass with her it is very easy to win your lane. I max her W first over Q since the damage is more reliable. When you do the triple hit (auto, double up, auto. like 99% sure that double up doesn't reset your attack timer, but i've had some weird things where i've autoed right after double up) you get a very significant chunk of magic damage out. It doesn't give you the same upfront burst that maxing double up gives you, but it gives you very high sustained damage that is very hard to keep up with. Also her ultimate is insanely good. It requires very good positioning to be effective, but if you are a little bit ahead and have some AoE ccs on your team, you can chunk people with your ult.
I would recommend them both really. I would say MF is much easier than draven, since you have to catch his axes to do the most possible damage (it's not always wise to catch the axe though). Because of that, cc disrupts his damage way more than it does other people. Neither of them have a mobility thing like a dash, but they both have MS buffs. Draven's is more reliable because it's an ability, but MF's is excellent for roaming the map. Imo she is one of the only, if not the only, ad that can roam effectively if you are ahead in your lane. She doesn't have an amazing wave clear that isn't her ult, but you can shove them haul to somewhere, and put some scary damage out very fast.
So, either really, but I would say MF. They are both good picks though.