There are a couple of things here to consider. The i5 actually has a turbo boost frequency of 2.6GHz. The 1.3GHz is the base clock. So off the bat if it makes you feel better your new chip will be 200MHz faster.
http://ark.intel.com/products/75028/Intel-Core-i5-4250U-Processor-3M-Cache-up-to-2_60-GHz
Now, synthetic benchmarks I do not nearly value as much as real world testing but without a specific review from a reputable source comparing exactly these two chips it's the next best thing we have access to and the i5 4250 benches a passmark rating score of 3463 vs the Core 2 Duo P8600 coming in at 1542.
3463/1542 = 2.42 times better for this benchmark comparison. Others may chime in devaluing synthetic benchmarks but I've already addressed that before listing the above info. Here are the links:
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core2+Duo+P8600+%40+2.40GHz&id=974
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core+i5-4250U+%40+1.30GHz&id=1944
To summarize I'd conclude easily that the i5 4250 is better to answer your question. However, you must conclude the price difference, other features you find important etc to make the decision to actually pull the trigger and go out and get it. Hope this helped you at least a little!
Also, to address adding an SSD that will speed up your boot up time and any programs that launch from it but you could make the same argument and do this to the newer laptop and enjoy the all around upgrade there too. Obviously keeping the older laptop isn't as fun but it's more cost effective. Good luck with whatever you decide!
Thanks,
Justin S.