How is Monero's network less secure than Bitcoin's network? Are there any plans in work to increase the security of Monero's network and will it ever match Bitcoin's network or surpass it?
The security of a PoW network is basically the amount of money needed to attack it. Bitcoin has had a lot of money poured into miners, and Monero nowhere as much.
As an idea of how much money would be needed to attack Monero via a 51% attack, see this post: How much money would be required to cloud mine 51% of the network hash rate?. The network hash rate was 21 MH/s at the time of that calculation, so the cost should now be 50% higher since we're now at about 31 MH/s. That gives you about 90 thousand dollars a day.
For Bitcoin, mining is performed by ASICs. We can find rough estimations of the total energy used by the Bitcoin network at http://www.allied-control.com/publications/Analysis_of_Large-Scale_Bitcoin_Mining_Operations.pdf, about 250 to 500 MW. Let's use 400 MW as a high middle ground. In a day, at a cost of, say, 10 USD cents a kWh (https://en.wikipedia.org/wiki/Electricity_pricing#Price_comparison) for the US as an example, we get 400e6 * 0.1 / 1000 * 24 = 960 thousand dollars a day.
Now, these are very back of the envelope calculations. Using one's own GPUs for Monero (same as is assumed for Bitcoin) probably decreases the cost to attack Monero, and the numbers for Bitcoin may be out of date. But it shows how the relative security of two PoW networks compare. Incidentally, take particular attention to how the hash rate of the two networks can't be compared, as they use different hashes (the very fast SHA256 vs the slow Cryptonight).
You might find a good answer in the question I posted just slightly before yours.