Hmmm, I guess it would boil down to your needs/goals and the typical rent vs. buy calculators. You might try running the numbers through the commonly recommended NYT rent vs. buy calculator and see what you come up with. Not knowing anything else about your situation, it's hard to say. For example, do you expect to stay in the area for a long time? Expecting your family to grow or needing more room? Expecting housing prices or rents in your area to appreciate? Commute costs from each?
Saving that extra $350/month on rent plus other home ownership expenses sounds good on the surface, but that could evaporate fairly quickly through rent increases over the next few years, or if you find you need a larger apartment to accommodate a growing family. And assuming you have some kind of conventional loan, at least a fair amount of your mortgage payment is paying down the principal and therefore building up equity/savings. So, there might not be quite as much (or any savings) as you anticipate by moving to an apartment. And if you end up only saving $100 a month or something like that, I'm not sure if it's worth it to you to move and give up some of the benefits of home ownership (like greater privacy and independence, for example).
Good luck!