This report shows that Mars is hit over 200 times a year by meteorites big and/or fast enough to leave a crater of typically 12.8 feet diameter.
Earth strikes of this size are thankfully much rarer, so yes: Mars is more at risk.
Possible reasons for this are:
a) Mars is "only" 100 million km from the asteroid belt, whereas Earth is 180 million km away;
b) The Earth is protected by its atmosphere, which causes most incoming nasties to burn up;
c) The Earth's moon is colossal compared to Mars's largest moon Phobos (and even more so compared to Deimos) and so will offer more protection, either physically or gravitationally. Note that this is a possible rather than probable effect :)
vsz ponders on whether there were more asteroids flying around in the past - check out the Late Heavy Bombardment.
There's an implication in the question that the asteroid strikes should be sizeable enough to leave an obvious crater but of course there are many more smaller strikes which leave little or no evidence. The Earth grows in mass by 37,000 to 78,000 tons per year from falling space material:
How many meteorites hit Earth each year? (Intermediate)
The factors which cause over 200 craters on Mars must also apply to the small and medium particles, so it's fun to speculate on how much weight Mars puts on per year...
The bonus question asks “Why might craters on Mars be more readily visible?”
1) The first possibility is that the meteor lands in the ocean. The Earth is quite badly named, as 78% of the surface area is actually not earth but water, so we can assume that 78% of our meteors land here. Water acts as really thick air and slows the meteor comparatively gently and it will fall to the seabed.
We don’t yet know how hot meteors are; a small, rocky meteor will be extremely hot on the surface due to air friction, but it won’t conduct this heat to its core. One with a greater metal content will conduct and so will hold more heat. In either case there are very few reports of meteors causing fires at the impact site, so they won’t create a noticeable amount of steam when they hit the sea. Unless you’re in the area it’s unlikely that 78% of our meteorites will be detected.
2) Of those that hit the land, the most probable fate is to be worn away by the weather, and only comparatively recent craters still exist.
3) As always, there’s “misc” category. The Manson crater in Iowa, USA (which was thought to have killed the dinosaurs) is covered by glacial till; the Chicxulub crater in Mexico (which really did kill the dinosaurs) is also buried (by limestone sediment) but has a tell-tale series of sinkholes (“cenotes”) around its rim.