I've shot both, and I highly prefer the 10/22. I'd not even consider the Remington mentioned earlier in this thread. It's not even in the same league as the other two.
I wanted to touch down on a few points.
Marlin generally has a better trigger out of the box, but 10/22 trigger is more easily improved with aftermarket parts (see #2 above).
While I don't really like the 10/22 trigger much at all, every Marlin 60 I've shot has been 10x worse. The triggers on the ones I've shot have been absolutely horrible. They have had a ton of travel in them before they break, they have felt gritty, and they have been heavy.
That being said, the trigger on the 10/22's I've shot have been far from great. They have also been heavy and had a long pull. However, I personally prefer them to the Marlin 60's I've shot. So I guess this is a personal preference. Both need a trigger job out of the box imo.
All Marlin 60s except very early models have a last shot bolt hold-open feature. The 10/22 lacks this, which absolutely bugs the heck out of some folks, since almost all other modern semi-auto firearms do it.
This is also a personal preference. The advantage to the 10/22 here is it's safe to dry fire, while most rifle manufacturers say don't dry fire rimfire rifles if they have a bolt hold open feature. I'd personally rather be able to dry fire it, but some others would rather it hold the bolt open.
All that being said, the Marlin 60's have been slightly more accurate on average out of the box than the 10/22's I've shot. However, the 10/22's haven't been any slouch in the accuracy department. With modifications the 10/22 can be made to be a lot more accurate.
The biggest thing I dislike about the Marlin 60 and what ruins it from being a great rifle imo is the crappy scope rails being built on. I absolutely hate that style scope rail and since it's built onto the gun you are forced to use them. I've found quite often when using that style setup the rings like to slide on the rails after repeated use. This doesn't help that there are a ton of recent reports of these rails being cut so they aren't straight which magnifies this problem. Since Remington took over it seems the quality of these has suffered.
On the 10/22 you can use whatever style scope base you'd like.