D600 + Kit Lens or OMD EM5 with Primes?

Hi all,

I am fairly new to photography, but understand the basic concepts.  I have used (borrowed) DSLR's (T2i) and an OMD.  I have not held the D600, though it looks a tad bigger than the T2i.

I am trying to decide which to purchase: the D600 with Kit lens ($2000) or the OMD EM5 with the Panasonic Leica 25.4 and Olympus 45 1.8, which would put me in the $2000 range, give or take.

Obviiously, the OMD has the size advantage.  But I'm trying to determine, beyond the size/weight issue, what would I be gaining by going with the D600, or alternatively, what will I be losing by going with the OMD?

I was comfortable using the OMD (even though the menu system is a bit complicated), would the D600 be much more complicated to operate for a beginner like me?

As my wife and I recently had our first child (a girl), my main purpose would be to capture pictures of her as a baby, toddler, etc...and use the camera for other family related events, as well as portraits of my wife and child.  A lot of indoor photography as a result, at least initially.  We had a photographer friend come in to take shots of our child using a D700 with the 50mm 1.8 (I believe) and I loved the results, though unfortunately the D700 does not do video which is a feature I would prefer to have.  Obviously, I understand there was a lot of technique involved and post processing, and it was not just the D700 doing the work.

I am trying to talk myself into the D600 and then eventually purchase an RX100 or something similar to use as backup when I don't want to take the D600 out of the house.  However, will I be content with the kit lens on the D600, or am I going to have to invest in full frame lenses to make the most of the D600, in which case costs will be more than $2000.

I was initially dead set on the OMD, but when I started doing the math, I started having second thoughts.

Any input would be greatly appreciate (especially from folks who have used both cameras/formats), including suggestions for other cameras that may be suitable for my needs.

Thanks!