It's the opposite. Web wallets are much less secure than Bitcoin Core and MultiBit.
The miners will confirm your TX when they get around to it. Don't worry, the transaction will confirm.
mining pools have enogh space per block to fit 4200 tx's per block.. yet its their greed that they only fill at most 1000 tx's your mindset is playing their game. their greed is the cause of delays. and they want you to pay them. we need to get some protocol code in that any tx that is ignored EG time stamp is older then 10 minutes. they should be sanctioned, not rewarded. the tx fee is not a requirement for atleast a decade, we should not be subsidizing mining pools. the 25btc is and should be their reward for mining, and the pools need to have a hard lesson about what bitcoin is truly about.
right now the miners are selling at a loss, just to pay their fiat lifestyles. making them fiat investors not bitcoin investors. they do not are about the future of bitcoin, just getting free money. we need to get the fiat greed mindset away from bitcoin, otherwise there is no point in having bitcoin.
by teaching mining pools to accept all transactions. and teaching them to stop selling bitcoins at a loss, thy can create the demand for bitcoin to increase (limiting supply) so that the price rise effect gives them the FIAT they need to cover costs. instead of letting them keep shooting themselves in the foot alltthe time making bitcoin less appealing.
the mindset of miners of 2009-2012 was great, but its going downhill and becoming more like the FIAT market. all because of the decisions made by mining pool owners. we are no longer in the independant thought and control of the solo mining era. and we need to get these under 15 individuals (pool mining owners) to take proper responsibilities for their decisions of greed