L.,
It sounds like you are really trying for balance here. What an excellent question.:)
I would go with what you know about your kids, first and foremost. Do they usually show good judgment? Can they reasonably keep track of time? Perhaps a digital watch with an alarm for one of them to wear would be helpful for everyone: they can go play for 20-30 minutes and then come back to do a quick 'check in'. If it were me and I had fairly responsible children, I'd let the 7 year old go only if the 10 year old is going too, otherwise the 7year old can stay within view outside with his new friends until you get a sense of how responsible he can be independently.
I would also pop in, from time to time, just have a look from a distance to see what is going on at the park. How are the kids interacting with each other? What's the atmosphere like? Ask the new friends their names. Get to know them and their parents, even if only casually.
I think kids this age need some time that they aren't being watched over all the time. Be sure to be very clear about the rules (no going over to another child's house; staying at the park or wherever it's agreed they will be-- they MUST come home and ask if they want to play elsewhere, etc.) and the consequences for breaking those rules. (Being grounded to indoors for the day, etc.) And remind them about safety rules as well (both physical and the 'be mindful if some adult is hanging out without kids' etc. The usual stuff.) If the boys continue to keep to your agreements and are playing well with the other kids--- and if the other kids seem friendly, this would be a great thing for everyone.
Asking my husband for his opinion, too, he agrees that if the neighborhood seems pretty safe, go for the 'graduated amounts of time' approach. He pointed out that when there are groups of kids together, they are usually safer in that group. Also, he agrees that with both your sons going together, certainly, but perhaps not the seven year old alone. There's a big difference between ten and seven.:)