Well, wizards will do a lot more damage, but they also have a lot more relevant spells to cast, with wide variance in damage and casting times, so spell priority and casting order will be a much bigger aspect of your effectiveness. Wizards get two root spells, an encounter root and a single-target root, so as long as you are careful, soloing should be fairly easy, assuming the MOB can be rooted. Note that once you reach max level, lots of named MOBs are immune to control effects, such as root, so you will need to kite them if you want to kill them (or just blow them up faster than they can kill you). You will likely never be able to solo epic MOBs on a wizard, if that is important to you.
Necromancer is a very different animal. Necros only really have about 6-9 spells you want to actually cast with any regularity, as many of their spells (especially the limited pets) are so bad that casting them will generally lower your DPS. Necromancers also have a built-in tank in their fighter pet, and the AA ability "Tainted Heals" will keep it alive through the apocalypse if need be. The only issue with a necromancer when soloing alongside your fighter pet is keeping aggro on the pet, which will often require you to throttle your own damage output significantly, making kill-speed slower. However, that is only relevant for soloing challenging MOBs, like yellow heroics or epics. If you are just mass-slaughtering trivial solo MOBs, you can bring out the mage pet and ruin them.
So basically, wizards are fun for nuking stuff dead and will do more damage if you're good at casting priority. Necromancers will allow you to solo more difficult content, but will not do as much overall damage. Wizards will need to rely on rooting and kiting, while necromancers have to learn how to micromanage the pet AI and deal with aggro control when soloing.
I have both classes at 90, and I personally prefer the necromancer, but I am a very independent player--I solo a lot, and I've played a monk as my main for over a decade, so I get withdrawal symptoms when I don't have Feign Death (Which necromancers do). Either one could be very enjoyable for the right person, so I suggest you give them both a try!