1) Calculate the average duty cycle and average current
For example,
average wake up period = 30min = 1800s
active period = 10s @ 120mA
-> average current = (1790s * 10uA + 10s * 120mA)/1800s = 680 uA
2) Now compare the efficiency of the LDO vs. switch mode supply: look at the consumption at 680 uA load.
It's very likely the LDO will be the winner, although some small, modern switchers with good light load modes could work out if the assumptions change (for example, more frequent wake-up).
If you are going to need, say, 3.0V output, you are going to drop only 0.65V average, and the linear solution offers max efficiency of about 80%, which is achievable in practice, too, by choosing a very low quiescent current part. It's almost impossible to beat that.
For extreme optimization, one could use a hybrid LDO + switcher solution, but probably not worth the complexity.
Peak dissipation of 1.2V*120mA = 144mW for < 15 sec, or 1.2V*400mA = 480mW for some milliseconds max I guess, should be thermally trivial to handle as well, for any LDO package.
Do take a close look at the dropout voltage at your max peak (400mA) load, remember that in order to fully utilize your 2000mAh cell, you'd like to want to take it down to about 3.0V. If your absolute minimum at load is already more than 2.7V, you may need to sacrifice a bit. But clearly LDO's with dropouts well over 300-400mV start hurting your battery life by not allowing you to run the battery empty, so aim for ~200mV dropouts. Your large battery capacity is helping here: 400mA is only 0.2C, so there is no need to discharge to very low voltages; stopping somewhere around 3.1V, maybe even 3.2V, already gets you close to 0% charge left.